On the edge metric dimension of graphs

WebThe concept of metric dimension is widely applied to solve various problems in the different fields of computer science and chemistry, such as computer networking, integer … 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 ...

On graphs with the maximum edge metric dimension

Web15 de mar. de 2024 · Remarks on the vertex and the edge metric dimension of 2-connected graphs Martin Knor1, Jelena Sedlar2;4, Riste Skrekovski 3;4 1 Slovak University of Technology in Bratislava, Bratislava, Slovakia 2 University of Split, Faculty of civil engineering, architecture and geodesy, Croatia 3 University of Ljubljana, FMF, 1000 … 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 … fitzroy architects https://adellepioli.com

The dominant edge metric dimension of graphs Tavakoli

Web17 de mar. de 2024 · The edge metric dimension e d i m ( G) of a graph G is the least size of an edge metric generator of G. In this paper, we give the characterization of all connected bipartite graphs with e d i m = n − 2, which partially answers an open problem of … 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 tree graph (B m, n ). We got = m (n+1)-2 for m>1 and n>2, = m (n+2)-2 for m>1 and n>2, and = m (n+1)-1 if m>1 and n>2. Content from this work may be used under the terms of the … Web1 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 … fitzroy and wenlock amber

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On the edge metric dimension of graphs

The dominant metric dimension of graphs - ScienceDirect

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. Web19 de dez. de 2024 · ABSTRACT. In this paper, we construct the new concept namely the complement edge metric dimension on the graph, which is the result of combining two concepts. The first concept is edge metric dimension and in the second concept is complement metric dimension. Let given a graph G = ( V ( G ), E ( G )) where V ( G) = …

On the edge metric dimension of graphs

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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 ... 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 …

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 … 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 jan. de 2024 · [4] V. Filipović, A. Kartelj and J. Kratica, Edge metric dimension of some generalized Petersen graphs, Results Math. 74 (2024) Article 182. 10.1007/s00025-019-1105-9 Search in Google Scholar [5] F. Harary and R.A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976) 191–195. Search in Google Scholar 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 ...

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 …

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 … fitzroy armsWeb14 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 … can i list my home on mlsWebAn 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 ... can i list my house on zillowWeb27 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 … can i list my nft on multiple marketplacesWeb1 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 … fitzroy art collectiveWebThe 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. fitzroy art schoolWeb1 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 … can i list myself as a dependent