Results 51 to 60 of about 8,830,736 (317)
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.
Chitra, P. Jeya Bala, Arumugam, S.
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New results on metric-locating-dominating sets of graphs [PDF]
, 2016 A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distanc es from the elements of S , and the minimum cardinality of such a set is called the metri c-location- domination number.
González, Antonio +2 more
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Fault-Tolerant Resolvability and Extremal Structures of Graphs
Mathematics, 2019 In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs with fault-tolerant metric dimension n, n − 1 , and 2, which are the lower and upper extremal cases.
Hassan Raza +3 more
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Bounds for metric dimensions of generalized neighborhood corona graphs
Heliyon, 2021 In this paper, the authors analysed metric dimensions of arbitrary graphs G★˜∧i=1|V(G)|Hi in which graphs G,H1,H2,…,H|V(G)| are non-trivial, G is connected, and ★˜ denotes generalized neighborhood corona operation.
Rinurwati, S.E. Setiawan, Slamin
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On Resolving Hop Domination in Graphs
European Journal of Pure and Applied Mathematics, 2021 A set S of vertices in a connected graph G is a resolving hop dominating set of G if S is a resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2.
Jerson Mohamad, Helen M. Rara
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Metric dimension of fullerene graphs
Electronic Journal of Graph Theory and Applications, 2019 A resolving set W is a set of vertices of a graph G(V, E) such that for every pair of distinct vertices u, v ∈ V(G), there exists a vertex w ∈ W satisfying d(u, w) ≠ d(v, w).
Shehnaz Akhter, Rashid Farooq
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The connected partition dimension of truncated wheels
AKCE International Journal of Graphs and Combinatorics, 2021 Let G be a connected graph. For a vertex v of G and a subset S of V(G), the distance between v and S is d(v, S) = min Given an ordered k-partition = of V(G), the representation of v with respect to is the k-vector If for each pair of distinct vertices ...
Lyndon L. Lazaro, Jose B. Rosario
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On 2-Resolving Sets in the Join and Corona of Graphs
European Journal of Pure and Applied Mathematics, 2021 Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set in G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions.
Jean Mansanadez Cabaro, Helen M. Rara
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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.
Subramanian, Hemalathaa +1 more
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Application of neutrosophic resolving sets in earthquake disaster management using neutrosophic graph models [PDF]
Neutrosophic Sets and SystemsNeutrosophic graphs are more suitable for modelling real-life situations because real world data is often uncertain, incomplete, inconsistent, or indeterminate and neutrosophic graphs are specifically designed to handle all of neutrosophic graphs, these ...
R. Shanmugapriya, R. Shanmugapriya
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