On the edge metric dimension of graphs

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August undefined, 2024

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 ... Web27 de fev. de 2024 · A general sharp upper bound on the edge metric dimension of hierarchical products G(U)⊓H is proved and several examples are provided which demonstrate how these two methods can be applied to obtain the edge metrics dimensions of some applicable graphs. Expand

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

Web1 de jul. de 2024 · A set S ⊆ V is an edge metric generator of a graph G (V, E) if for any two distinct edges e 1, e 2 ∈ E there is a vertex s ∈ S such that s distinguishes e 1 and e … 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 … how to reset iphone 6 to factory settings

Graphs with the edge metric dimension smaller than the

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. 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 dimension (DEMD for short) is introduced and its basic properties are studied. Moreover, NP-hardness of computing DEMD of connected graphs is proved. Furthermore, this ... Web27 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 … how to reset iphone if disabled

The dominant edge metric dimension of graphs - ResearchGate

The dominant metric dimension of graphs - ScienceDirect

Web23 de fev. de 2024 · Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due to the non-unique, high-dimensional nature of graphs and the complex, non-local dependencies … Web20 de out. de 2024 · In a graph G, cardinality of the smallest ordered set of vertices that distinguishes every element of V (G) is the (vertex) metric dimension of G. Similarly, the cardinality of such a set is the edge metric dimension of G, if it distinguishes E(G). In this paper these invariants are considered first for unicyclic graphs, and it is shown that the … north carolina wofford gameWeb1 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 … north carolina withholding tax registration

"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 … " - On the edge metric dimension of graphs

On the edge metric dimension of graphs

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

Web10 de abr. de 2024 · Signal Variation Metrics and Graph Fourier Transforms for Directed Graphs. Laura Shimabukuro, Antonio Ortega. Published 10 April 2024. Mathematics, … Web24 de set. de 2024 · Edge metric dimension of some graph operations. Let be a connected graph. Given a vertex and an edge , the distance between and is defined as . A nonempty set is an edge metric generator for if for any two edges there is a vertex such that . The minimum cardinality of any edge metric generator for a graph is the edge …

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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 … 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 ...

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. Web1 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 …

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 ... 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 …

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 …

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 … how to reset iphone if screen is frozenWeb1 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 … how to reset iphone forgot pwWeb31 de dez. de 2024 · The edge metric dimension of the graph G is at least r = 2 m + n. We now continue with the following lemmas which constitutes the heart of our NP … north carolina women\u0027s basketball rosterWebwww.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 ... how to reset iphone after emergency sosWeb1 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 … how to reset iphone itunes lockWeb1 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 ... north carolina wolfpack basketballWeb11 de nov. de 2024 · We also computed the fault-tolerant edge metric dimension of path, cycle, complete graph, cycle with chord graph, tadpole graph and kayak paddle graph. Home {{subColumn.name}} AIMS Mathematics. Search ... Uniquely identifying the edges of a graph: The edge metric dimension, Discrete Appl. Math., 251 (2024), 204-220. doi: … north carolina woman death