Results 11 to 20 of about 60,505 (275)
Independent resolving sets in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 Let be a connected graph. Let be a subset of V with an order imposed on W. The k-vector is called the resolving vector of v with respect to W. The set W is called a resolving set if for any two distinct vertices In this paper we investigate the existence
B. Suganya, S. Arumugam
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Edge Version of Metric Dimension and Doubly Resolving Sets of the Necklace Graph
Mathematics, 2018 Consider an undirected and connected graph G = ( V G , E G ) , where V G and E G represent the set of vertices and the set of edges respectively.
Jia-Bao Liu +3 more
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On classes of neighborhood resolving sets of a graph [PDF]
Electronic Journal of Graph Theory and Applications, 2018 Let G = (V, E) be a simple connected graph. A subset S of V is called a neighbourhood set of G if G = ⋃s ∈ S < N[s] > , where N[v] denotes the closed neighbourhood of the vertex v in G. Further for each ordered subset S = {s1, s2, ..., sk} of V and
B. Sooryanarayana, Suma A. S.
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Secure Resolving Sets in a Graph [PDF]
Symmetry, 2018 Let G = (V, E) be a simple, finite, and connected graph. A subset S = {u1, u2, …, uk} of V(G) is called a resolving set (locating set) if for any x ∈ V(G), the code of x with respect to S that is denoted by CS (x), which is defined as CS (x) = (d(u1, x), d(u2, x), .., d(uk, x)), is different for different x.
Hemalathaa Subramanian +1 more
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Resolving Sets without Isolated Vertices
Procedia Computer Science, 2015 AbstractLet G be a connected graph. Let W = (w1, w2, ..., wk ) be a subset of V with an order imposed on it. For any v ∈ V, the vector r(v|W) = (d(v, w1), d(v, w2), ..., d(v, wk )) is called the metric representation of v with respect to W. If distinct vertices in V have distinct metric representations, then W is called a resolving set of G.
S Arumugam
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Resolving sets for Johnson and Kneser graphs [PDF]
European Journal of Combinatorics, 2013 A set of vertices $S$ in a graph $G$ is a {\em resolving set} for $G$ if, for any two vertices $u,v$, there exists $x\in S$ such that the distances $d(u,x) \neq d(v,x)$. In this paper, we consider the Johnson graphs $J(n,k)$ and Kneser graphs $K(n,k)$, and obtain various constructions of resolving sets for these graphs. As well as general constructions,
Delia Garijo +2 more
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Power graphs and exchange property for resolving sets
Open Mathematics, 2019 Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given.
Abbas Ghulam +4 more
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Error-Correcting Codes from k-Resolving Sets [PDF]
Discussiones Mathematicae Graph Theory, 2019 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.
Bailey Robert F., Yero Ismael G.
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Maximal resolving sets in a graph
International Journal of Mathematics for IndustryLet G be a connected graph. A subset [Formula: see text] of [Formula: see text] is called a resolving set of G if the code of any vertex [Formula: see text] with respect to S is different from the code of any other vertex where code of u with respect to ...
V. Swaminathan, R. Sundareswaran
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A Study on Minimal Doubly Resolving Sets of Certain Families of Networks
IEEE Access, 2023 The suppression of harmful information and even its diffusion can be predicted and delayed by precisely finding sources with limited resources. The doubly resolving sets (DRSs) play a crucial role in determining where diffusion occurs in a network ...
Muhammad Ahmad +3 more
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