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On the Existence of a Cyclic Near-Resolvable (6n+4)-Cycle System of 2K12n+9
<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>
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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 ...
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Uniform coverings of 2-paths with 4-cycles
<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>
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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. ...
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Error-correcting codes from k-resolving sets
<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>
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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 . ...
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Strong metric dimension of generalized Jahangir graph
[article]
<span title="2019-05-10">2019</span>
<i >
arXiv
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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. ...
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Error-correcting codes from k-resolving sets
[article]
<span title="2017-08-25">2017</span>
<i >
arXiv
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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 . ...
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An Extension Theorem for Closing Maps of Shifts of Finite Type
<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>
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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 ...
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An extension theorem for closing maps of shifts of finite type
<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>
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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 ...
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Covers of Non-Almost-Finite Type Sofic Systems
<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>
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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.) ...
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Covers of non-almost-finite type sofic systems
<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>
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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.) ...
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The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs
<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>
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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. ...
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Resolvent Estrada index of cycles and paths
<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>
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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. ...
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Partition dimension and strong metric dimension of chain cycle
[article]
<span title="2020-07-18">2020</span>
<i >
arXiv
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<span class="release-stage" >pre-print</span>
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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. ...
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The strong metric dimension of graphs and digraphs
<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>
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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 . ...
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Directed Metric Dimension of Oriented Graphs with Cyclic Covering
[article]
<span title="2014-04-21">2014</span>
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arXiv
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<span title="2014-01-05">2014</span>
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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 ...
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On classes of neighborhood resolving sets of a graph
<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>
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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. ...
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