Results 21 to 30 of about 146,548 (294)
Fault-Tolerant Metric Dimension of Circulant Graphs
Mathematics, 2022 Let G be a connected graph with vertex set V(G) and d(u,v) be the distance between the vertices u and v. A set of vertices S={s1,s2,…,sk}⊂V(G) is called a resolving set for G if, for any two distinct vertices u,v∈V(G), there is a vertex si∈S such that d ...
Laxman Saha +4 more
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Certain Varieties of Resolving Sets of A Graph [PDF]
Journal of the Indonesian Mathematical Society, 2021 Let G=(V,E) be a simple connected graph. For each ordered subset S={s_1,s_2,...,s_k} of V and a vertex u in V, we associate a vector Gamma(u/S)=(d(u,s_1),d(u,s_2),...,d(u,s_k)) with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if Gamma(u/S) not equal to Gamma(v/S) for all u, v in V-S ...
Sooryanarayana, Badekara +2 more
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Unicyclic graphs with non-isolated resolving number $2$ [PDF]
Transactions on Combinatorics, 2023 Let $G$ be a connected graph and $W=\{w_1, w_2,\ldots,w_k\}$ be an ordered subset of vertices of $G$. For any vertex $v$ of $G$, the ordered $k$-vector $$r(v|W)=(d(v,w_1), d(v,w_2),\ldots,d(v,w_k))$$ is called the metric representation of $v$ with ...
Mohsen Jannesari
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The dominant metric dimension of graphs
Heliyon, 2020 The G be a connected graph with vertex set V(G) and edge set E(G). A subset S⊆V(G) is called a dominating set of G if for every vertex x in V(G)∖S, there exists at least one vertex u in S such that x is adjacent to u.
Liliek Susilowati +4 more
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The metric dimension for resolving several objects [PDF]
, 2022 A set of vertices S is a resolving set in a graph if each vertex has a unique array of distances to the vertices of S. The natural problem of finding the smallest cardinality of a resolving set in a graph has been widely studied over the years.
Laihonen T
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On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
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Determining Sets, Resolving Sets, and the Exchange Property [PDF]
Graphs and Combinatorics, 2009 A subset U of vertices of a graph G is called a determining set if every automorphism of G is uniquely determined by its action on the vertices of U. A subset W is called a resolving set if every vertex in G is uniquely determined by its distances to the vertices of W. Determining (resolving) sets are said to have the exchange property in G if whenever
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Application of Metric Dimensions to Minimize the Installation of Fire Sensors on The Rectorate Building of Pasifik Morotai University [PDF]
MATEC Web of Conferences, 2022 The metric dimension of the connected graph G for each 𝑣 𝜖 𝑉(𝐺) to the set W is . The set r (ν|W) = (d(ν, w1), d(ν,w2),…d(ν,wk) W is called the resolving set if every vertex u,v in G, if u ≠ ν , then r (u|W) ≠ r (ν|W) .
Parera Cicilya Orissa F. +3 more
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Resolving domination in graphs [PDF]
, 2003 summary:For an ordered set $W =\lbrace w_1, w_2, \cdots , w_k\rbrace $ of vertices and a vertex $v$ in a connected graph $G$, the (metric) representation of $v$ with respect to $W$ is the $k$-vector $r(v|W) = (d(v, w_1),d(v, w_2) ,\cdots , d(v, w_k ...
Dutton, Ronald D. +3 more
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Bounds on the domination number and the metric dimension of co-normal product of graphs
Journal of Inequalities and Applications, 2018 In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph GH $G_{H}$ of two simple graphs G and H in terms of parameters associated with G and H.
Imran Javaid +2 more
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