Results 1 to 10 of about 669,922 (254)
Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs
Mathematics, 2022 The vertex (respectively edge) metric dimension of a graph G is the size of a smallest vertex set in G, which distinguishes all pairs of vertices (respectively edges) in G, and it is denoted by dim(G) (respectively edim(G)). The upper bounds dim(G)≤2c(G)−
Martin Knor +2 more
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On Mixed Metric Dimension of Some Path Related Graphs
IEEE Access, 2020 A vertex $k\in V_{G}$ determined two elements (vertices or edges) $\ell,m \in V_{G}\cup E_{G}$ , if $d_{G}(k,\ell)\neq d_{G}(k,m)$ . A set $R_ {\text {m}}$ of vertices in a graph $G$ is a mixed metric generator for $G$ , if two distinct elements
Hassan Raza, Ying Ji, Shaojian Qu
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Study of modified prism networks via fractional metric dimension
AIMS Mathematics, 2023 For a connected network $ \Gamma $, the distance between any two vertices is the length of the shortest path between them. A vertex $ c $ in a connected network is said to resolve an edge $ e $ if the distances of $ c $ from its endpoints are unequal ...
Ahmed Alamer +2 more
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The Metric Dimension and Local Metric Dimension of Relative Prime Graph
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2020 This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime.
Inna Kuswandari +2 more
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Graphs with mixed metric dimension three and related algorithms
AIMS Mathematics, 2023 Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $.
Dalal Awadh Alrowaili +3 more
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Metric and Fault-Tolerant Metric Dimension of Hollow Coronoid
IEEE Access, 2021 Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons.
Ali N. A. Koam +3 more
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Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2)
Frontiers in Physics, 2020 Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or
Hassan Raza, Ying Ji
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Study of Convexo-Symmetric Networks via Fractional Dimensions
IEEE Access, 2022 For having an in-depth study and analysis of various network’s structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters ...
Muhammad Kamran Aslam +3 more
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Contemporary Mathematics and Applications (ConMathA), 2020 Adjacency metric dimension and local adjacency metric dimension are the development of metric dimension. The purpose of this research is to determine the adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H ...
Virdina Rahmayanti +2 more
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Metric dimension of Andrásfai graphs [PDF]
Opuscula Mathematica, 2019 A set \(W\subseteq V(G)\) is called a resolving set, if for each pair of distinct vertices \(u,v\in V(G)\) there exists \(t\in W\) such that \(d(u,t)\neq d(v,t)\), where \(d(x,y)\) is the distance between vertices \(x\) and \(y\).
S. Batool Pejman +2 more
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