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On the Edge Metric Dimension of Certain Polyphenyl Chains

Muhammad Ahsan, Zohaib Zahid, Dalal Alrowaili, Aiyared Iampan, Imran Siddique, Sohail Zafar, Haidar Ali
<span title="2021-12-18">2021</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/d464oyarorcjjdsif2szpik6ti" style="color: black;">Journal of Chemistry</a> </i> &nbsp;
In this paper, we calculate the edge metric dimension of ortho-polyphenyl chain graph O n , meta-polyphenyl chain graph M n , and the linear [n]-tetracene graph T n and also find the edge metric dimension  ...  The minimum number of vertices in W E is known as the edge metric dimension of G .  ...  Nadeem et al. computed the metric dimension of the ortho-polyphenyl chain, meta-polyphenyl chain, and para-polyphenyl chain graphs in [11] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2021/3855172">doi:10.1155/2021/3855172</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5jdxu6edozdvbemjy7gemm4ahe">fatcat:5jdxu6edozdvbemjy7gemm4ahe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220114132302/https://downloads.hindawi.com/journals/jchem/2021/3855172.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/88/e0/88e01717925c742d61cc76034572e4da8d223f6b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2021/3855172"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

Fault-Tolerant Resolvability of Certain Crystal Structures

Sathish Krishnan, Bharati Rajan
<span title="">2016</span> <i title="Scientific Research Publishing, Inc,"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t35nyaf3lzb6lei7onyd4hnf4e" style="color: black;">Applied Mathematics</a> </i> &nbsp;
In this paper we determine the metric dimension and fault-tolerant metric dimension problems for the graphs of certain crystal structures.  ...  A resolving set W for G is fault-tolerant if W\{v} is also a resolving set, for each v in W, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set.  ...  [4] have proved that the metric dimension of a d-dimensional grid is d, generalizing the result of Melter et al. [3] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/am.2016.77055">doi:10.4236/am.2016.77055</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ssvkzkd5zrezbbyqg7zrf5ykey">fatcat:ssvkzkd5zrezbbyqg7zrf5ykey</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170923084542/http://file.scirp.org/pdf/AM_2016042515583550.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c1/2f/c12f7114b01b5c5cb17711dd41846c8c0dce0f14.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4236/am.2016.77055"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

QoC-based Optimization of End-to-End M-Health Data Delivery Services

Ing Widya, Bert-jan Beijnum, Alfons Salden
<span title="">2006</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mnyfrpct5rf6xjio5dwvrxuttu" style="color: black;">IEEE International Workshop on Quality of Service, IWQoS</a> </i> &nbsp;
We propose min-max-plus based algebraic QoC models for computing the quality of delivered data impeded by the QoS of the resources along the alternative delivery paths.  ...  To rank all the possible resource configurations and therewith select from those the most optimal one(s) we introduce a workflow management metric based on the quality dimensions like freshness and availability  ...  ACKNOWLEDGMENT Authors thank Masja Kempen for improving the quality of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iwqos.2006.250476">doi:10.1109/iwqos.2006.250476</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iwqos/WidyaBS06.html">dblp:conf/iwqos/WidyaBS06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4vsgqrz73zdpnagyhcotzk6kuy">fatcat:4vsgqrz73zdpnagyhcotzk6kuy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719162530/https://ris.utwente.nl/ws/files/5337385/iwqos06_123_QoC_cready_final_awareness.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/b7/77b7356e67b959be8ee84d86261dbf71024f9d1d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iwqos.2006.250476"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Computing the metric dimension of a graph from primary subgraphs

Dorota Kuziak, Juan Alberto Rodríguez-Velázquez, González Ismael Yero
<span title="">2017</span> <i title="Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g64zvtslcjdqncvrfbmvf422qi" style="color: black;">Discussiones Mathematicae Graph Theory</a> </i> &nbsp;
It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices.  ...  The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.  ...  For instance, assume that Computing the Metric Dimension of a Graph from ... 277 A(G i ) = {v}.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7151/dmgt.1934">doi:10.7151/dmgt.1934</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/stdljdw5qrd7xnjsl3by4rowy4">fatcat:stdljdw5qrd7xnjsl3by4rowy4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200824030501/https://content.sciendo.com/downloadpdf/journals/dmgt/37/1/article-p273.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/75/af/75af2aa737b6630c30f6ca4f0857fc1e1e52fe13.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7151/dmgt.1934"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs

Dorota Kuziak
<span title="2020-08-02">2020</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ye33srllvnanjouxn4tmrfgjsq" style="color: black;">Mathematics</a> </i> &nbsp;
The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G.  ...  To study the strong metric dimension of graphs, a very important role is played by a structure of graphs called the strong resolving graph In this work, we obtain the strong metric dimension of some families  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/math8081266">doi:10.3390/math8081266</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zknfnp27wjeglfpnltfxvei7xe">fatcat:zknfnp27wjeglfpnltfxvei7xe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200806105826/https://res.mdpi.com/d_attachment/mathematics/mathematics-08-01266/article_deploy/mathematics-08-01266.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ca/53/ca5367709c458be2eb724009b036954f61e99585.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/math8081266"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Edge Resolvability of Crystal Cubic Carbon Structure [article]

Sahil Sharma, Vijay Kumar Bhat, Sohan Lal
<span title="2022-05-02">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The resolvability parameters for graph G= (V,E) are a relatively new advanced field in which the complete structure is built so that each vertex (atom) or edge (bond) represents a distinct position.  ...  In this article, we study the resolvability parameters i.e., edge resolvability of chemical graph of crystal structure of cubic carbon CCS(n)  ...  The problem of computing the edge metric dimension of CCS(n) and certain generalisations of these graphs is discussed in this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2205.00648v1">arXiv:2205.00648v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vzxs7vizb5efthgo2zmarv2uum">fatcat:vzxs7vizb5efthgo2zmarv2uum</a> </span>
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Computing the metric dimension of a graph from primary subgraphs [article]

D. Kuziak, J. A. Rodríguez-Velázquez, I. G. Yero
<span title="2015-02-10">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It is well known that the problem of finding the metric dimension of a graph is NP-Hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices.  ...  The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.  ...  This suggests obtaining closed formulae for the metric dimension of special nontrivial families of graphs, or bounding the value of this invariant as tight as possible, or reducing the problem of computing  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1309.0641v2">arXiv:1309.0641v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hkd7ai7vs5fu3oa5rtzdbfzyli">fatcat:hkd7ai7vs5fu3oa5rtzdbfzyli</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200827192202/https://arxiv.org/pdf/1309.0641v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/88/57/885787ca9f0b7e2ef5be34ff8fa21b14d5743c78.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1309.0641v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Topological Properties of few Poly Oxide, Poly Silicate, DOX and DSL Networks

F. Simonraj, A. George
<span title="">2013</span> <i title="EJournal Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hvh5w7m2xzcrhkbhz4hppekzju" style="color: black;">International Journal of Future Computer and Communication</a> </i> &nbsp;
The fourth section contains the proof of the minimum metric dimension of regular triangulene oxide network to be 2.  ...  The first section deals with the introduction to (Resolving number) minimum metric dimension problems, and few related work about Silicate networks.  ...  It was noted in [20] that determining the minimum metric dimension problem (resolving number) of a graph is an NP-complete problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7763/ijfcc.2013.v2.128">doi:10.7763/ijfcc.2013.v2.128</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z4qqfjrk4jendohwldimkpu2oa">fatcat:z4qqfjrk4jendohwldimkpu2oa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812110553/http://ijfcc.org/papers/128-IT0034.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bb/4c/bb4cfb5a58b710d5faccbd891f2eeef400b86c53.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7763/ijfcc.2013.v2.128"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Moduli of tropical plane curves

Sarah Brodsky, Michael Joswig, Ralph Morrison, Bernd Sturmfels
<span title="2015-04-09">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6h56sattgbatpozuefrob6v4ji" style="color: black;">Research in the Mathematical Sciences</a> </i> &nbsp;
It has dimension 2g+1 unless g ≤ 3 or g = 7. We compute these spaces explicitly for g ≤ 5.  ...  We study the moduli space of metric graphs that arise from tropical plane curves. There are far fewer such graphs than tropicalizations of classical plane curves.  ...  MJ received support from the Einstein Foundation Berlin and the Deutsche Forschungsgemeinschaft. RM and BS were supported by the US National Science Foundation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s40687-014-0018-1">doi:10.1186/s40687-014-0018-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/53niicyi5fe75hqxpcncar553a">fatcat:53niicyi5fe75hqxpcncar553a</a> </span>
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Page 1612 of Mathematical Reviews Vol. , Issue 2003C [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
However, the structure of metric spaces of higher dimension is not so well understood. Indeed, even 2-dimensional finite metric spaces can have a rich structure.  ...  Harary et al. defined the Euclidean dimension of a graph G as the minimum nonnegative integer n for which G is a unit graph in the Euclidean n-space R”. “Recently, H.  ... 
<span class="external-identifiers"> </span>
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Computing the local metric dimension of a graph from the local metric dimension of primary subgraphs [article]

Juan A. Rodríguez-Velázquez, Carlos García Gómez and Gabriel A. Barragán-Ramírez
<span title="2014-02-02">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that the computation of the local metric dimension of a graph with cut vertices is reduced to the computation of the local metric dimension of the so-called primary subgraphs.  ...  A minimum local metric generator is called a local metric basis for G and its cardinality the local metric dimension of G.  ...  In this paper we show that the computation of the local metric dimension of a graph with cut vertices is reduced to the computation of the local metric dimension of the so-called primary subgraphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1402.0177v1">arXiv:1402.0177v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gvfcpnkb6fgi5apsgpejxana3u">fatcat:gvfcpnkb6fgi5apsgpejxana3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826021344/https://arxiv.org/pdf/1402.0177v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3f/e5/3fe5c568a6d16e8528797927294405e4f3dbc197.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1402.0177v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Visualizing energy landscapes with metric disconnectivity graphs

Lewis C. Smeeton, Mark T. Oakley, Roy L. Johnston
<span title="2014-05-28">2014</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/72zcmi3smndcrdvxgve7ny6ytq" style="color: black;">Journal of Computational Chemistry</a> </i> &nbsp;
Acknowledgments The computations described in this paper were performed using the University of Birminghams BlueBEAR HPC service, which provides a High-Performance Computing service to the Universitys  ...  See http://www.birmingham.ac.uk/bear for more details. The authors thank Prof. David Wales for helpful discussions, and Dr. Victor Ruhle and Dr.  ...  The ith Isomap metric corresponds to the ith embedded dimension of the low-dimensional manifold of fr a g Ut .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jcc.23643">doi:10.1002/jcc.23643</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24866379">pmid:24866379</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4285870/">pmcid:PMC4285870</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ctflnzfwwrg3jmft52wuqqqgey">fatcat:ctflnzfwwrg3jmft52wuqqqgey</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200305091413/https://research.birmingham.ac.uk/portal/files/16481390/Smeeton_Visualizing_energy_landscapes_JCC_2014.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/39/ac/39acc3dfc61aaa4549baa24f4be0b7a6b16ad0d1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jcc.23643"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4285870" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Cyber Security Analytics: A Stochastic Model for Security Quantification Using Absorbing Markov Chains

Subil Abraham, Suku Nair
<span title="">2014</span> <i title="Engineering and Technology Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x35svotye5crdo2d6qzxuyyq7m" style="color: black;">Journal of Communications</a> </i> &nbsp;
Most of the Attack graph based metrics proposed in the literature are one dimensional; however the research community has acknowledged the fact that security needs to be treated as a multidimensional concept  ...  In this paper, we utilize stochastic modeling techniques using Attack graphs to define a complementary suite of quantitative metrics to aid the security engineer in visualizing the current as well as future  ...  Probabilistic Path (PP) metric: is another dimension which measures the likelihood of an attacker to reach the absorbing states of the graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12720/jcm.9.12.899-907">doi:10.12720/jcm.9.12.899-907</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3hf2ntgpanaodpazz7etjm4ldm">fatcat:3hf2ntgpanaodpazz7etjm4ldm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150927233519/http://www.jocm.us/uploadfile/2014/1231/20141231022619157.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/36/a6/36a6ece237ef1961e720a5def26507b6916c0938.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12720/jcm.9.12.899-907"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Matrices, shortest paths, minimal cuts and Euclidian metric for undirected graphs

Victor A. Rusakov
<span title="">2018</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cx3f4s3qmfe6bg4qvuy2cxezyu" style="color: black;">Procedia Computer Science</a> </i> &nbsp;
If using the Euclidean norm one gets an advantage in doing analysis and synthesis of graphs in comparison to traditional metrics.  ...  The proposed metric can be used to generate the behaviour of intelligent agents.  ...  These values represent the shortest paths between s and t, but in another metric [4] . Ergodic Markov chains. Graph metrics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.procs.2018.11.104">doi:10.1016/j.procs.2018.11.104</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tdmbgyi6jrh5rf7ylw6ca7ivze">fatcat:tdmbgyi6jrh5rf7ylw6ca7ivze</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191114052424/https://pdf.sciencedirectassets.com/280203/1-s2.0-S1877050918X00222/1-s2.0-S1877050918323925/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBUaCXVzLWVhc3QtMSJHMEUCIQDF1tKymitL0ufSbOCcbrzUqz%2F3%2FEH9z0hA2NGYV67jcgIgAP0IGt3dZmlWzKuLizPrrjlzF0RmLIxkv%2FX8ZgfYrO8q0QIIPhACGgwwNTkwMDM1NDY4NjUiDH1L9izEKPuIeV59LyquAjUT3y3EkVcG7VsoROB1C%2FDpNZk35n%2Bm%2BM8gDmjyvN8ZrHfeyNkydGdhXAfrrAxttuigkm3vRYbszFRdffRNoX8pDxsDVMXMpfiXIx9yzKL6xWk903ViZA9rgO98iD2c7tgBr%2BvFmqN3226p2pXfjfStNQiB71sm7OFZEHB3%2FuwLa5zhbxV3M5EhNrPEYEiCUnm8LKvCr%2BzIeofpruP26wGMuvJl2zudlWZiZoUjxKALLs1%2F9VZmTnU4Vgp55EANrQXJYocFNR7xqQKcVqJ7RAzEOEc9xyoNbhkBORHmd4QuyoahWB%2BXstW2qfNxBOE1Vf%2B0xsmoQkhkGcDTWmW7kvoD8OdX%2FHvBa2zCVm2wBZG%2B6EmukFNzEB02KcUCRQw8yokLT5QCTUDwy%2Boy1YG%2BMMyxs%2B4FOs4CzxI2Wc62xYrOl1wAu6bSe5SoGJUdkktjW5wpABzBSaovwtXeoLpsn91JejsZJQwY0Hziox0QVrwisAp3Hme1bpdliJeuv8sQ4EXrGUM60Ae86E%2Fy8pqSuH4UpbDTCxINnVZRKfNZWgRzwTgpXAgT8yzkrFYfmjrKl9%2FnlClDL%2F5XYoXWlX1xp14QxgVtJ9sjKxwztdfWylaHs%2BkAA42QcyD7A25OcgZlVb9Zpc73dS5zZGG2iZBQbD5M%2FOJaWkcvG3FFTQx7eE9DVZMWePTKKqEZLcjUg%2B2amXf0GACizbd4AbkWpAs4gNuRbuL3AtOFs7Rn%2BIk9%2Bzj3VcN8QjUE8pw%2B%2FZDKbQ9P4kmwMXMj3HNyx%2BOnKCYc4EeiOYWeZGZmlhGNAp85JhAF2JdiCvOGP97vBza3%2F5HD9GYsuIaRjaWiR4cSFCTFbzFUpBlRQw%3D%3D&amp;X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20191114T052424Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=300&amp;X-Amz-Credential=ASIAQ3PHCVTYTBSNXSEO%2F20191114%2Fus-east-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=d730b1a8a18d57f719ef665fec2dd90ace644857d833bff349eee4d1c969a980&amp;hash=98d7a02549a51ae4e44e0b270cb02b0489ead998f8dbd25de3fbe0a91cdbbb74&amp;host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&amp;pii=S1877050918323925&amp;tid=spdf-7757396e-4d9a-4604-a87f-69bb91c4b041&amp;sid=551d854a8772384d8b89e614a4218ff90338gxrqa&amp;type=client" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f1/01/f1018343e993c03f1f8716f8fbb84622f24efb16.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.procs.2018.11.104"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

On reduction of graphs and Markov chain models

Yunwen Xu, Srinivasa M. Salapaka, Carolyn L. Beck
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">IEEE Conference on Decision and Control and European Control Conference</a> </i> &nbsp;
This paper introduces a new method for reducing large directed graphs to simpler graphs with fewer nodes.  ...  The reduction is carried out through node and edge aggregation, where the simpler graph is representative of the original large graph.  ...  A critical difference lies in the difficulty of formulating a cost function since this requires defining a metric that compares two graphs (the original and the reduced) that are of different dimensions  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2011.6160882">doi:10.1109/cdc.2011.6160882</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/XuSB11.html">dblp:conf/cdc/XuSB11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mbsd6dzr6zcx7lrylnckgim5mu">fatcat:mbsd6dzr6zcx7lrylnckgim5mu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814162145/http://folk.ntnu.no/skoge/prost/proceedings/cdc-ecc-2011/data/papers/1243.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3c/51/3c515f1e66de5fcbbffb8f46ceaacdab2dfadb30.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2011.6160882"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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