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On the Existence of a Cyclic Near-Resolvable (6n+4)-Cycle System of 2K12n+9

Raja'i Aldiabat, Haslinda Ibrahim, Sharmila Karim
<span title="2019-08-01">2019</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5etzjnhqc5b3ricneysxmg2p6e" style="color: black;">Journal of Mathematics</a> </i> &nbsp;
In this article, we prove the existence of a simple cyclic near-resolvable v-1/2-cycle system of 2Kv for v≡9 mod 12 by the method of constructing its starter.  ...  This work is partially financially supported by the Universiti Utara Malaysia through the Fundamental Research Grant Scheme (FRGS) [Code: 14198].  ...  Simple Cyclic Near-Resolvable (6 +4)-Cycle System of 2 12 +9 In this section, we prove, explicitly and directly, the existence of a simple cyclic near-resolvable (6 + 4)-cycle system of 2 12 +9 by constructing  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2019/5276753">doi:10.1155/2019/5276753</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kaz6arx2cjgrdg4puxvgccsdmm">fatcat:kaz6arx2cjgrdg4puxvgccsdmm</a> </span>
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Uniform coverings of 2-paths with 4-cycles

Midori Kobayashi, Keiko Kotani, Nobuaki Mutoh, Gisaku Nakamura
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xgh73r267rawppi7nsz4lx3nxq" style="color: black;">AKCE International Journal of Graphs and Combinatorics</a> </i> &nbsp;
A D(G, H, λ) design is a multiset D of subgraphs of G each isomorphic to H so that every 2-path [directed 2-path] of G lies in exactly λ subgraphs in D.  ...  → C 4 are a 4-cycle and a directed 4-cycle, respectively. c ⃝ 2015 Kalasalingam University.  ...  Since the number of directed 2-paths of K * n,n is 2n 2 (n −1), we see that every directed 2-path of K * n,n lies on exactly one directed 4-cycle in C. Hence C is a D(K * n,n , − → C 4 , 1) design.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.akcej.2015.06.011">doi:10.1016/j.akcej.2015.06.011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hzbfv2c5ofg2ffkpgdk7s6yyb4">fatcat:hzbfv2c5ofg2ffkpgdk7s6yyb4</a> </span>
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Error-correcting codes from k-resolving sets

Robert Bailey, González Ismael Yero
<span title="">2018</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;
We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, and present a decoding algorithm which makes use of covering designs.  ...  Along the way, we determine the k-metric dimension of grid graphs (i.e. Cartesian products of paths). MSC 2010: 05C12, 94B25 (primary); 05B40, 94B35 (secondary).  ...  diameter of a cycle C n being (approximately) half that of a path P n .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7151/dmgt.2087">doi:10.7151/dmgt.2087</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/subevll35rgnfegy7cskuhlubq">fatcat:subevll35rgnfegy7cskuhlubq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190308175430/http://pdfs.semanticscholar.org/f72e/f9977036f14a98485198dc8bd88d319a9d96.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/f7/2e/f72ef9977036f14a98485198dc8bd88d319a9d96.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7151/dmgt.2087"> <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>

Strong metric dimension of generalized Jahangir graph [article]

Rashid Farooq, Naila Mehreen
<span title="2019-05-10">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A set W ⊆ V(G) is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of W.  ...  A vertex w∈ V(G) strongly resolves two vertices u,v ∈ V(G) if v belongs to a shortest u-w path or u belongs to a shortest v-w path.  ...  Acknowledgment Authors are thankful to the Higher Education Commission of Pakistan for financial support to carry out this research under grant No. 20-3067/NRPU/R&D/HEC/12.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1905.03975v1">arXiv:1905.03975v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xshd4465afgwhhdp6xg37hupcq">fatcat:xshd4465afgwhhdp6xg37hupcq</a> </span>
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Error-correcting codes from k-resolving sets [article]

Robert F. Bailey, Ismael G. Yero
<span title="2017-08-25">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, and present a decoding algorithm which makes use of covering designs.  ...  Along the way, we determine the k-metric dimension of grid graphs (i.e. Cartesian products of paths).  ...  diameter of a cycle C n being (approximately) half that of a path P n .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1605.03141v4">arXiv:1605.03141v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nf5dk3wqhvbtrkqzr6i2fm5geu">fatcat:nf5dk3wqhvbtrkqzr6i2fm5geu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200916151815/https://arxiv.org/pdf/1605.03141v4.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/c8/c6/c8c60f7768682e976ca4ec04bb9087e136553bd1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1605.03141v4" 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>

An Extension Theorem for Closing Maps of Shifts of Finite Type

Jonathan Ashley
<span title="">1993</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w3g32txdvneltemssag5nwfxcy" style="color: black;">Transactions of the American Mathematical Society</a> </i> &nbsp;
If there exists some right-closing factor map n : ZA -» J.B between aperiodic shifts of finite type, then any right-closing map ip : X -► HB from any shift of finite type X contained in Z,A can be extended  ...  to a right-closing factor map from all of ZA onto Zb ■ We prove this and give some consequences.  ...  If an isolated cycle SoSX---sp-X is split by legal rounds of state splitting into a graph y with all lean states, then y is a cycle of trees that forms a resolving covering graph of Sb , covering Sb with  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2154352">doi:10.2307/2154352</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i6cnn724pbecfh7mgxomucbenu">fatcat:i6cnn724pbecfh7mgxomucbenu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170826044644/http://www.ams.org/journals/tran/1993-336-01/S0002-9947-1993-1105064-9/S0002-9947-1993-1105064-9.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/83/46/8346c25ca3ff59875974a98e0a46e152bdac786b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2154352"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> jstor.org </button> </a>

An extension theorem for closing maps of shifts of finite type

Jonathan Ashley
<span title="1993-01-01">1993</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w3g32txdvneltemssag5nwfxcy" style="color: black;">Transactions of the American Mathematical Society</a> </i> &nbsp;
If there exists some right-closing factor map n : ZA -» J.B between aperiodic shifts of finite type, then any right-closing map ip : X -► HB from any shift of finite type X contained in Z,A can be extended  ...  to a right-closing factor map from all of ZA onto Zb ■ We prove this and give some consequences.  ...  If an isolated cycle SoSX---sp-X is split by legal rounds of state splitting into a graph y with all lean states, then y is a cycle of trees that forms a resolving covering graph of Sb , covering Sb with  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-1993-1105064-9">doi:10.1090/s0002-9947-1993-1105064-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4mnoqrrvkfbkjhioaoay5krl54">fatcat:4mnoqrrvkfbkjhioaoay5krl54</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170826044644/http://www.ams.org/journals/tran/1993-336-01/S0002-9947-1993-1105064-9/S0002-9947-1993-1105064-9.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/83/46/8346c25ca3ff59875974a98e0a46e152bdac786b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9947-1993-1105064-9"> <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>

Covers of Non-Almost-Finite Type Sofic Systems

Susan Williams
<span title="">1988</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
that no two are intercepted by a common cover of S.  ...  The authors asked whether a non-AFT sofic system has a finite collection C of covers such that every cover is intercepted by a cover in C.  ...  Let a; be a resolving word for n which labels a path in J from state 4 to state 1 in Figure 2 . (If these states are the same we must avoid choosing x = swlt.)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2047495">doi:10.2307/2047495</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ulq7ngbxojburkkur4uzzco6uy">fatcat:ulq7ngbxojburkkur4uzzco6uy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814053436/http://www.ams.org/journals/proc/1988-104-01/S0002-9939-1988-0958076-3/S0002-9939-1988-0958076-3.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/30/03/30038e13fd8343afa4b0c0ee105d2486ede7cbd8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2047495"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> jstor.org </button> </a>

Covers of non-almost-finite type sofic systems

Susan Williams
<span title="1988-01-01">1988</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
that no two are intercepted by a common cover of S.  ...  The authors asked whether a non-AFT sofic system has a finite collection C of covers such that every cover is intercepted by a cover in C.  ...  Let a; be a resolving word for n which labels a path in J from state 4 to state 1 in Figure 2 . (If these states are the same we must avoid choosing x = swlt.)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1988-0958076-3">doi:10.1090/s0002-9939-1988-0958076-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cp5q7h2h6jdqnlw5eynfx4vvme">fatcat:cp5q7h2h6jdqnlw5eynfx4vvme</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814053436/http://www.ams.org/journals/proc/1988-104-01/S0002-9939-1988-0958076-3/S0002-9939-1988-0958076-3.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/30/03/30038e13fd8343afa4b0c0ee105d2486ede7cbd8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1988-0958076-3"> <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;
A set S of vertices of G is a strong resolving set for G if every two distinct vertices of G are strongly resolved by a vertex of S.  ...  A vertex w of a connected graph G strongly resolves two distinct vertices u,v∈V(G), if there is a shortest u,w path containing v, or a shortest v,w path containing u.  ...  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>

Resolvent Estrada index of cycles and paths

Bo Deng, Shouzhong Wang, Ivan Gutman
<span title="">2016</span> <i title="Centre for Evaluation in Education and Science (CEON/CEES)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hmfxgtje5bhzviiahtrezxtrfa" style="color: black;">Scientific Publications of the State University of Novi Pazar Series A Applied Mathematics Informatics and mechanics</a> </i> &nbsp;
Let G be a simple graph of order n. The resolvent Estrada index of G is defined as . . , λ n are the eigenvalues of G. Formulas for computing EE r of the cycle C n and the path P n are derived.  ...  The precision of these approximations are shown to be excellent. We also examine the difference and relations between the Estrada index and the resolvent Estrada index of C n and P n .  ...  This research was supported by the Science and Technology Project of Maoming City no. 001-423217050-5020, and by the Introduction of Talent Project no. 513085.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5937/spsunp1601001d">doi:10.5937/spsunp1601001d</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2mkf334ndjhytjhvh7htyypztu">fatcat:2mkf334ndjhytjhvh7htyypztu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180722171212/https://scindeks-clanci.ceon.rs/data/pdf/2217-5539/2016/2217-55391601001D.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/85/b3/85b3a1339f4ec72e975464fe8763fd573ffc6970.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5937/spsunp1601001d"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Partition dimension and strong metric dimension of chain cycle [article]

Talmeez Ur Rehman, Naila Mehreen
<span title="2020-07-18">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we determine the partition dimension and strong metric dimension of a chain cycle constructed by even cycles and a chain cycle constructed by odd cycles.  ...  A vertex w∈ V(G) strongly resolves two distinct vertices u,v ∈ V(G) if u belongs to a shortest v-w path or v belongs to a shortest u-w path.  ...  We would also like to thank the Higher Education Commission of Pakistan to support this research under grant No. 20-3067/NRPU /R&D/HEC/12.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.09499v1">arXiv:2007.09499v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bycanztoina6hcgidac4pg7pya">fatcat:bycanztoina6hcgidac4pg7pya</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200824200355/https://arxiv.org/pdf/2007.09499v1.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/d0/ac/d0ac6764614f6f9b3235e5859199576954fecd33.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.09499v1" 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>

The strong metric dimension of graphs and digraphs

Ortrud R. Oellermann, Joel Peters-Fransen
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
A set W of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of W.  ...  A vertex w is said to strongly resolve a pair u, v of vertices of G if there exists some shortest u-w path containing v or some shortest v-w path containing u.  ...  To see this suppose n 4 and that D is the n-cycle v 1 , v 2 , . . . , v n , v 1 and D the digraph obtained from the n-cycle v 1 , v 2 , . . . , v n , v 1 by adding the arc v 3 v 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2006.06.009">doi:10.1016/j.dam.2006.06.009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/drqglo6lyrbpjpbpgatsb6jmlq">fatcat:drqglo6lyrbpjpbpgatsb6jmlq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171004075924/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/db9/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDE2NjIxOHgwNjAwMzAxNQ%3D%3D.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/f7/44f7ac0688b3846283399cd6fd70633a08ce8194.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2006.06.009"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Directed Metric Dimension of Oriented Graphs with Cyclic Covering [article]

Sigit Pancahayani, Rinovia Simanjuntak
<span title="2014-04-21">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
If any two distinct vertices u,v satisfy r(u|B)≠ r(v|B), then B is said to be a resolving set of D.  ...  This paper deals with metric dimensions of oriented wheels, oriented fans, and amalgamation of oriented cycles, all of which admitting C_n-simple orientations.  ...  A path amalgamation of cycles in C, denoted by P x − Amal{C ni } t i=1 , where 2 ≤ x ≤ min{|V (C ni )|} − 1, is the graph constructed by joining the cycles in C on a common path or order x called the terminal  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1401.0929v2">arXiv:1401.0929v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fc5s5l42qbd6nnazlmim7vj3xi">fatcat:fc5s5l42qbd6nnazlmim7vj3xi</a> </span>
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On classes of neighborhood resolving sets of a graph

B. Sooryanarayana, Suma A. S.
<span title="2018-04-03">2018</span> <i title="The Institute for Research and Community Services (LPPM) ITB"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lpemckh6jfhehiaagnsspj5vmu" style="color: black;">Electronic Journal of Graph Theory and Applications</a> </i> &nbsp;
The purpose of this paper is to introduce various types of nr-sets and compute minimum cardinality of each set, in possible cases, particularly for paths and cycles.  ...  A subset S is said to be resolving set of G if Γ(u/S) = Γ(v/S) for all u, v ∈ V − S. A neighbouring set of G which is also a resolving set for G is called a neighbourhood resolving set (nr-set).  ...  Ambedkar Institute of Technology, Bengaluru, for their constant support during the preparation of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5614/ejgta.2018.6.1.3">doi:10.5614/ejgta.2018.6.1.3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/skxnosztbngarneigxglyuu54u">fatcat:skxnosztbngarneigxglyuu54u</a> </span>
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