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Double edge resolving set and exchange property for nanosheet structure [PDF]
HeliyonThe exploration of edge metric dimension and its applications has been an ongoing discussion, particularly in the context of nanosheet graphs formed from the octagonal grid. Edge metric dimension is a concept that involves uniquely identifying the entire
Ali N.A. Koam +4 more
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Resolving set and exchange property in nanotube
AIMS Mathematics, 2023 Give us a linked graph, $ G = (V, E). $ A vertex $ w\in V $ distinguishes between two components (vertices and edges) $ x, y\in E\cup V $ if $ d_G(w, x)\neq d_G (w, y). $ Let $ W_{1} $ and $ W_{2} $ be two resolving sets and $ W_{1} $ $ \neq $ $ W_{2} $.
Ali N. A. Koam +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.
B. Sooryanarayana +2 more
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A Study on Fuzzy Resolving Domination Sets and Their Application in Network Theory
Mathematics, 2023 Consider a simple connected fuzzy graph (FG) G and consider an ordered fuzzy subset H = {(u1, σ(u1)), (u2, σ(u2)), …(uk, σ(uk))}, |H| ≥ 2 of a fuzzy graph; then, the representation of σ − H is an ordered k-tuple with regard to H of G. If any two elements
Manimozhi Vasuki +3 more
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A Study of Independency on Fuzzy Resolving Sets of Labelling Graphs
Mathematics, 2023 Considering a fuzzy graph G is simple and can be connected and considered as a subset H=u1,σu1,u2,σu2,…uk,σuk, |H|≥2; then, every two pairs of elements of σ−H have a unique depiction with the relation of H, and H can be termed as a fuzzy resolving set ...
Ramachandramoorthi Shanmugapriya +3 more
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Optimal Multi-Level Fault-Tolerant Resolving Sets of Circulant Graph C(n : 1, 2)
Mathematics, 2023 Let G=(V(G),E(G)) be a simple connected unweighted graph. A set R⊂V(G) is called a fault-tolerant resolving set with the tolerance level k if the cardinality of the set Sx,y={w∈R:d(w,x)≠d(w,y)} is at least k for every pair of distinct vertices x,y of G ...
Laxman Saha +4 more
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On the Characterization of a Minimal Resolving Set for Power of Paths
Mathematics, 2022 For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w).
Laxman Saha +4 more
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Topological insights into breast cancer drugs: a QSPR approach using resolving topological indices [PDF]
Frontiers in ChemistryIntroductionBreast cancer, one of the most prevalent malignancies in women begins in the milk ducts or lobules and is divided into invasive and non-invasive variants.
E. Pandeeswari, J. Ravi Sankar
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ALGORITHM FOR FINDING DOMINATION RESOLVING NUMBER OF A GRAPH [PDF]
Journal of Mechanics of Continua and Mathematical SciencesA minimum resolving set is a resolving set with the lowest cardinality and its cardinality is a dimension of connected graph , represented by . A dominating set is a set of vertices such that each of is either in or has at least one neighbor in ...
Iqbal M. Batiha +2 more
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Metric Dimension, Minimal Doubly Resolving Sets, and the Strong Metric Dimension for Jellyfish Graph and Cocktail Party Graph [PDF]
Complex, 2020 Let Γ be a simple connected undirected graph with vertex set VΓ and edge set EΓ. The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely ...
Jia Liu, Ali Zafari, Hassan Zarei
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