On the edge metric dimension of graphs

Author: gqys

August undefined, 2024

WebThe size of a dominant edge metric basis of G is denoted by D d i m e ( G ) and is called the dominant edge metric dimension. In this paper, the concept of dominant edge metric dimension (DEMD for short) is introduced and its basic properties are studied. Moreover, NP-hardness of computing DEMD of connected graphs is proved. Web8 de abr. de 2024 · 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 ...

On the edge dimension and the fractional edge dimension of …

WebThe size of a dominant edge metric basis of G is denoted by Ddime(G) and is called the dominant edge metric dimension. In this paper, the concept of dominant edge metric … Web1 de ago. de 2024 · Some primary studies on the edge metric dimension of Cartesian product graphs were presented in , where the value of the edge metric dimension was … incoming images

A note on the metric and edge metric dimensions of 2-connected graphs

Web1 de abr. de 2013 · In graph theory, metric dimension is a parameter that has appeared in various applications, as diverse as network discovery and verification [2], strategies for … Web31 de dez. de 2024 · The edge metric dimension of graph is the minimum cardinality of edge resolving set, say , and is denoted as . An edge metric generator for of … incoming ice storm

Asymptotic Behavior of the Edge Metric Dimension of the Random Graph

The dominant edge metric dimension of graphs - ResearchGate

Web31 de jan. de 2016 · We prove that computing the edge metric dimension of connected graphs is NP-hard and give some approximation results. Moreover, we present some … Web15 de fev. de 2015 · The effect of vertex and edge deletion on the edge metric dimension of graphs. 03 January 2024. Meiqin Wei, Jun Yue & Lily Chen. Edge Metric Dimension of Some Generalized Petersen ... C. X., Yi, E.: The fractional strong metric dimension of graphs. Lecture Notes in Comput. Sci., 8287, 84–95 (2013) Article MathSciNet Google ... incoming imap serverWeb10 de abr. de 2024 · Signal Variation Metrics and Graph Fourier Transforms for Directed Graphs. Laura Shimabukuro, Antonio Ortega. Published 10 April 2024. Mathematics, Computer Science. In this paper we consider the problem of constructing graph Fourier transforms (GFTs) for directed graphs (digraphs), with a focus on developing multiple … incoming income

"Web1 de jul. de 2024 · Given a connected graph G ( V , E ), the edge dimension, denoted edim ( G ), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the … " - On the edge metric dimension of graphs

On the edge metric dimension of graphs

[1612.06936] On the edge metric dimension for the random graph …

Web1 de jul. de 2024 · Given a connected graph G ( V , E ), the edge dimension, denoted edim ( G ), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the sense that the edges have pairwise different tuples of distances to the vertices of S. The notation was introduced by Kelenc, Tratnik, and Yero, and in their paper they posed several ... Web1 de jun. de 2024 · As a natural counterpart, Kelenc et al. [9] introduced the concept of edge metric dimension and proved that the decision problem of computing the edge metric …

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Web1 de ago. de 2024 · Although determining the metric dimension of an arbitrary graph is a complex computational task, exact formulae and upper bounds exist for some specific families of graphs, the readers can refer ... Web31 de dez. de 2024 · Furthermore, the k-size edge metric dimension of the graphs Pm Pn, Pm Cn for m, n ≥ 3 and the generalized Petersen graph is determined. It is shown that these families of graphs have constant k ...

Web21 de dez. de 2016 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … WebThe metric dimension dim(G) of a graph G is the minimum cardinality of a set of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. Let v and e respectively denote a vertex and an edge of a graph G. We show that, for any integer k, there exists a graph G such that dim(G − v) − dim(G) = k.

Web1 de mar. de 2024 · In this paper, we examined complement metric dimension of particular tree graphs such as caterpillar graph (C mn ), firecrackers graph (Fmn), and banana … Web31 de mar. de 2024 · An edge metric generator of a connected graph G is a vertex subset S for which every two distinct edges of G have distinct distance to some vertex of S, where …

Web3 de jan. de 2024 · DOI: 10.1007/s10878-021-00838-7 Corpus ID: 245654396; The effect of vertex and edge deletion on the edge metric dimension of graphs @article{Wei2024TheEO, title={The effect of vertex and edge deletion on the edge metric dimension of graphs}, author={Meiqin Wei and Jun Yue and Lily Chen}, …

WebAn edge metric generator containing a minimum number of vertices is called an edge metric basis for G and the cardinality of an edge metric basis is called the edge metric dimension denoted by $$\mu _ {E} (G)$$μE (G). In this paper, we study the edge metric dimension of some classes of plane graphs. It is shown that the edge metric dimension ... incoming iii corps commanderWeb21 de out. de 2024 · Abstract: The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every … incoming imapWeb1 de jan. de 2024 · The edge metric dimension of a graph is introduced based on the distance of edges of the graph. As a main result we computed edge metric dimension … incoming imap for outlookWeb14 de dez. de 2015 · The concept of k-metric generator was introduced by the authors of this paper in [] as a generalization of the standard concept of metric generator.In graph theory, the notion of metric generator was previously given by Slater in [19, 20], where the metric generators were called locating sets, and also, independently by Harary and … incoming imap server for outlookWeb1 de mar. de 2024 · 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.An ordered set W ⊆ V (G) is called a resolving set of G, if every pair of vertices u and v in V (G) have distinct … incoming imap settingsWeb1 de mai. de 2024 · The local edge metric dimension of G, denoted by dim E (G), is a local edge metric generator of G if for every pair xk,ky of adjacent edges of G. Our … incoming imap server for yahoo mailWeb21 de dez. de 2016 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. incoming in french