On the edge metric dimension of graphs

Author: zeht

August undefined, 2024

WebDownloadable! 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 ) ≤ 2 c ( G ) − 1 and edim ( G ) ≤ 2 c ( G ) − 1 , where c ( G ) denotes the cyclomatic number of G … Web31 de mar. de 2024 · An edge metric basis of G is an edge metric generator of G of cardinality dim e ( G). It is trivial to see that for any connected graph G of order n the following holds: 1 ≤ dim e ( G) ≤ n − 1. Graphs for which dim e ( G) = n − 1 are called topful. An edge metric generator S is not necessarily a metric generator.

The dominant metric dimension of graphs - ScienceDirect

Web29 de out. de 2024 · It is suggested to study the following references for better comprehension and details of metric dimension of graphs [11–16]. A lot of work has … Web10 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 … song lyrics i am redeemed

On the edge metric dimension of convex polytopes and its related graphs

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. 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 … Web28 de out. de 2024 · An 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 … song lyrics i am not sick but i am not well

The k -Metric Dimension of Corona Product Graphs - Springer

The dominant edge metric dimension of

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. Web1 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 … song lyrics i am the god of hellfireWeb1 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 ... song lyrics i am the god that healeth thee

"Web4 de out. de 2024 · The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge … " - On the edge metric dimension of graphs

On the edge metric dimension of graphs

The dominant edge metric dimension of graphs - ResearchGate

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 … Web14 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 …

Did you know?

Web21 de out. de 2024 · The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to the graph. The extra edge can either be selected adversarially, in which … Webwww.ejgta.org Electronic Journal of Graph Theory and Applications 11 (1) (2024), 197–208 The dominant edge metric dimension of graphs Mostafa Tavakolia, Meysam Korivand b, Ahmad Erfanian ...

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 … 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 ...

Web21 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. Web21 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 …

Web1 de ago. de 2024 · Knor M, Majstorović S, Toshi A, S̆krekovski R, Yero I (2024) Graphs with the edge metric dimension smaller than the metric dimension. Appl Math Comput …

Web18 de dez. de 2024 · DOI: 10.1155/2024/3855172 Corpus ID: 245338040; On the Edge Metric Dimension of Certain Polyphenyl Chains @article{Ahsan2024OnTE, title={On the Edge Metric Dimension of Certain Polyphenyl Chains}, author={Muhammad Ahsan and Zohaib Zahid and Dalal Awadh Alrowaili and Aiyared Iampan and Imran Siddique and … smallest hearing aidWeb27 de fev. de 2024 · For a given graph , the metric and edge metric dimensions of , and , are the cardinalities of the smallest possible subsets of vertices in such that they … smallest hearing aid 2021Web3 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}, … song lyrics i am the lord that healeth theeWeb1 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 ... song lyrics i am the righteous hand of godWeb1 de mai. 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 … song lyrics i am womanWeb1 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 … smallest headphones noise cancellingWeb1 de fev. de 2024 · The edge metric dimension of G, denoted by dimE ( G ), is the minimum cardinality of edge metric generator for G. As a main result, we provide some results of edge metric dimension on some families of tree graph, namely star graph, broom graph, double broom graph, and banana tree graph. Content from this work may … smallest head size tennis racket