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On the Adjacent Eccentric Distance Sum Index of Graphs

Hui Qu, Shujuan Cao, Vince Grolmusz
<span title="2015-06-19">2015</span> <i title="Public Library of Science (PLoS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s3gm7274mfe6fcs7e3jterqlri" style="color: black;">PLoS ONE</a> </i> &nbsp;
In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as independence number, covering number, vertex connectivity, chromatic number,  ...  For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively.  ...  Acknowledgments The authors are grateful to anonymous referees from helpful comments to an earlier version of this manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pone.0129497">doi:10.1371/journal.pone.0129497</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26091095">pmid:26091095</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4474630/">pmcid:PMC4474630</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g46hcjrjprdgpjxqz6w5dorkk4">fatcat:g46hcjrjprdgpjxqz6w5dorkk4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191201225715/http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC4474630&amp;blobtype=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/e3/87/e3872563f913fceaf0aeca60b82db29094466cf2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pone.0129497"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> plos.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4474630" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Page 5313 of Mathematical Reviews Vol. , Issue 2000h [page]

<span title="">2000</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;
In the paper a function N(k, A, D), the largest size of a graph of degree at most A and k-diameter D, is studied.  ...  Summary: “In the minimum sum coloring problem, the goal is to color the vertices of a graph with the positive integers such that the sum of all colors is minimal.  ... 
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On the extremal properties of the average eccentricity

Aleksandar Ilić
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nkrwe4pmozafvnd72yxufztpku" style="color: black;">Computers and Mathematics with Applications</a> </i> &nbsp;
The average eccentricity is deeply connected with a topological descriptor called the eccentric connectivity index, defined as a sum of products of vertex degrees and eccentricities.  ...  The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc(G) of a graph G is the mean value of eccentricities of all vertices of G.  ...  Acknowledgments This work was supported by Research Grant 144007 of Serbian Ministry of Science and Technological Development.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.camwa.2012.04.023">doi:10.1016/j.camwa.2012.04.023</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zynxb3yjnvbknaw3yacfkt7egy">fatcat:zynxb3yjnvbknaw3yacfkt7egy</a> </span>
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Chain Hexagonal Cacti with the Extremal Eccentric Distance Sum

Hui Qu, Guihai Yu
<span title="">2014</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nxzqpsogkbe55mjq33syzghf2e" style="color: black;">The Scientific World Journal</a> </i> &nbsp;
Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph.  ...  In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of lengthn, respectively.  ...  [3] studied the various lower and upper bounds for the EDS in terms of other graph invariants including the Wiener index, the degree distance, the eccentric connectivity index, independence number,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2014/897918">doi:10.1155/2014/897918</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/24741365">pmid:24741365</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3972840/">pmcid:PMC3972840</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3d4yc3yubbgllnwacekamj4yei">fatcat:3d4yc3yubbgllnwacekamj4yei</a> </span>
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On the eccentric distance sum of graphs

Aleksandar Ilić, Guihai Yu, Lihua Feng
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7a65khxirfbfljbnqng5zzeslu" style="color: black;">Journal of Mathematical Analysis and Applications</a> </i> &nbsp;
In Section 4 various lower and upper bounds for the eccentric distance sum in terms of other graph invariants (the Wiener index, the degree distance, eccentric connectivity index, independence number,  ...  Furthermore, the authors characterized the extremal trees with minimal and second minimal eccentric distance sum in the class of trees with given diameter.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jmaa.2011.02.086">doi:10.1016/j.jmaa.2011.02.086</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sdcimbelznbrrlhha2iqtex6o4">fatcat:sdcimbelznbrrlhha2iqtex6o4</a> </span>
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Eccentric Connectivity Index and Polynomial of Some Graphs

A. Bindusree, V. Lokesha, P. Ranjini
<span title="2015-01-10">2015</span> <i title="Sciencedomain International"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jsookdmc2ffbna6ldqrknyxsri" style="color: black;">British Journal of Mathematics &amp; Computer Science</a> </i> &nbsp;
Let G be a simple and connected graph with n vertices and m edges. The Eccentric connectivity index of G is defined as the summation of the product of degree and eccentricity of the vertices [15] .  ...  In addition to it, a lower bound of these invariants for the subdivision graph of the double graph of a given graph and a lower bound of these invariants for the extended double cover graph of a given  ...  In addition, the extremal trees with given diameter and minimal eccentric distance sum is also characterized.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.9734/bjmcs/2015/15137">doi:10.9734/bjmcs/2015/15137</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tuf2wfstnvgijhodi6h3j5f7nq">fatcat:tuf2wfstnvgijhodi6h3j5f7nq</a> </span>
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On the extremal properties of the average eccentricity [article]

Aleksandar Ilic
<span title="2011-06-15">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The average eccentricity is deeply connected with a topological descriptor called the eccentric connectivity index, defined as a sum of products of vertex degrees and eccentricities.  ...  The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc (G) of a graph G is the mean value of eccentricities of all vertices of G.  ...  This work was supported by Research Grant 144007 of Serbian Ministry of Science and Technological Development.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1106.2987v1">arXiv:1106.2987v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4ogt7zcwsve7jhm5leud7lepwy">fatcat:4ogt7zcwsve7jhm5leud7lepwy</a> </span>
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Distance Degree Regular Graphs and Distance Degree Injective Graphs: An Overview

Medha Itagi Huilgol
<span title="">2014</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ukdw2rc3qreyhlaihgmrddedzu" style="color: black;">Journal of Discrete Mathematics</a> </i> &nbsp;
Thus, the sequence(di0,di1,di2, ..., dij,...)is the distance degree sequence of the vertexviinGwheredijdenotes the number of vertices at distancejfromvi.  ...  Thedistance degree sequence (dds)of a vertexvin a graphG = (V, E)is a list of the number of vertices at distance1, 2, ... . , e(v)in that order, wheree(v)denotes the eccentricity ofvinG.  ...  Conflict of Interests The author declares that there is no conflict of interests regarding the publication of this paper.  ... 
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Eccentric connectivity index [article]

Aleksandar Ilić
<span title="2011-03-13">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In addition, we present explicit formulae for the values of eccentric connectivity index for several families of composite graphs and designed a linear algorithm for calculating the eccentric connectivity  ...  It is defined as ξ^c (G) = ∑_v ∈ V (G) deg (v) ·ϵ (v) , where deg (v) and ϵ (v) denote the vertex degree and eccentricity of v , respectively.  ...  This work was supported by the Research grant 144007 of the Serbian Ministry of Science and Technological Development.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1103.2515v1">arXiv:1103.2515v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/diyzacypuzc5zbajfjkk7zzefq">fatcat:diyzacypuzc5zbajfjkk7zzefq</a> </span>
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On the difference between the eccentric connectivity index and eccentric distance sum of graphs [article]

Yaser Alizadeh, Sandi Klavžar
<span title="2020-05-06">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The eccentric connectivity index of a graph G is ξ^c(G) = ∑_v ∈ V(G)ε(v)(v), and the eccentric distance sum is ξ^d(G) = ∑_v ∈ V(G)ε(v)D(v), where ε(v) is the eccentricity of v, and D(v) the sum of distances  ...  Regular graphs with diameter at most 2 and joins of cocktail-party graphs with complete graphs form the graphs that attain the two equalities, respectively.  ...  Acknowledgements Sandi Klavžar acknowledges the financial support from the Slovenian Research Agency (research core funding P1-0297 and projects J1-9109, J1-1693, N1-0095).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.02635v1">arXiv:2005.02635v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/infcq3sya5dgvecerv2olw732a">fatcat:infcq3sya5dgvecerv2olw732a</a> </span>
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Distance in Graphs [chapter]

Wayne Goddard, Ortrud R. Oellermann
<span title="2010-09-16">2010</span> <i title="Birkhäuser Boston"> Structural Analysis of Complex Networks </i> &nbsp;
The distance between two vertices is the basis of the definition of several graph parameters including diameter, radius, average distance and metric dimension.  ...  We also discuss characterizations of graph classes described in terms of distance or shortest paths. Finally, generalizations are considered.  ...  Acknowledgments We would like to thank Peter Dankelmann for sharing his thoughts on average distance with us.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-0-8176-4789-6_3">doi:10.1007/978-0-8176-4789-6_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b4xawt5qhzakbizso6yfhyfpxi">fatcat:b4xawt5qhzakbizso6yfhyfpxi</a> </span>
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On radially extremal graphs and digraphs, a survey

Ferdinand Gliviak
<span title="">2000</span> <i title="Institute of Mathematics, Czech Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fyro42zjjfbelgnkwq562pisde" style="color: black;">Mathematica Bohemica</a> </i> &nbsp;
Estimate the number of edges, the maximum degree and the minimum degree of either a decreasing graph or a maximal graph. 2.3. Radius stable graphs.  ...  , the properties of distances d,d mm ,d max ,d sum and d* were studied in several papers, e.g  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.21136/mb.2000.125959">doi:10.21136/mb.2000.125959</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hwe4rrxunrdpfnyjcgr5zmp6iq">fatcat:hwe4rrxunrdpfnyjcgr5zmp6iq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200309234933/https://dml.cz/bitstream/handle/10338.dmlcz/125959/MathBohem_125-2000-2_10.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/44/0b/440b1a128f98af03f25becd696b5dd2f3fcc3203.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.21136/mb.2000.125959"> <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 Harary index of trees [article]

Aleksandar Ilić, Guihai Yu, Lihua Feng
<span title="2011-05-21">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also characterize the extremal trees with maximal Harary index with respect to the number of vertices of degree two, matching number, independence number, radius and diameter.  ...  The Harary index of a graph G is recently introduced topological index, defined on the reverse distance matrix as H(G)=∑_u,v ∈ V(G)1/d(u,v), where d(u,v) is the length of the shortest path between two  ...  In [1] the authors obtained some lower and upper bounds for the Harary index of graphs in terms of the diameter and the number of connected components.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.0920v3">arXiv:1104.0920v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4iuyiunl4jc3fdyjm4aq4zry7m">fatcat:4iuyiunl4jc3fdyjm4aq4zry7m</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1104.0920/1104.0920.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> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8b/f8/8bf834c07ef9e58b7efa67fbb1cfa720c67f6e05.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.0920v3" 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>

On the Solvability of the Six Degrees of Kevin Bacon Game [chapter]

Michele Borassi, Pierluigi Crescenzi, Michel Habib, Walter Kosters, Andrea Marino, Frank Takes
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
10-100 BFSes instead of |V | BFSes (independent of the value of |V |), and thus having running time O(|E|).  ...  In this paper, we will propose a new algorithm that computes the radius and the diameter of a graph G = (V, E), by finding bounds through heuristics and improving them until exact values can be guaranteed  ...  Answering the above questions is equivalent to computing the diameter and the radius of a graph, where the diameter is the maximum distance between two connected vertices, and the radius is the distance  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-07890-8_5">doi:10.1007/978-3-319-07890-8_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u4urppl77fhi5gnoxxnnorqrw4">fatcat:u4urppl77fhi5gnoxxnnorqrw4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160706131120/http://liacs.leidenuniv.nl:80/~takesfw/pdf/fun2014.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/88/2b/882b6be0dae3ca487720c14249bd2029fe3f6371.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-07890-8_5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Five results on maximizing topological indices in graphs [article]

Stijn Cambie
<span title="2021-11-08">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that the maximum for the difference of the Wiener index and the eccentricity is attained by the path if the order n is at least 9 and that the maximum weighted Szeged index of graphs of given  ...  We determine the extremal graphs attaining the maximal generalized Wiener index (e.g. the hyper-Wiener index) among all graphs with given matching number or independence number.  ...  Acknowledgements The author is very grateful to the anonymous referees for the time they dedicated to this article and for the comments they made which improved this manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.03864v4">arXiv:2005.03864v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uwrrxpp2ybgmrpwokm57lknuki">fatcat:uwrrxpp2ybgmrpwokm57lknuki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211110090614/https://arxiv.org/pdf/2005.03864v4.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/9b/dc/9bdc10e975660e0ae916960d0d9108e4f023d235.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.03864v4" 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>
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