On the edge metric dimension of graphs

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August undefined, 2024

Web15 de jul. de 2024 · Given a connected graph G, the metric (resp. edge metric) dimension of G is the cardinality of the smallest ordered set of vertices that uniquely identifies every …

The fractional metric dimension of permutation graphs

Web1 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 … 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 ... eal holdings sdn bhd

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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 … 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 … 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 … cso office bellingham wa

Fault-tolerant edge metric dimension of certain families of graphs

Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs

Web6 de ago. de 2024 · Analogous to resolving function and fractional metric dimension, we introduce edge resolving function and fractional edge (metric) dimension as follows. A … 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 … cso nst thailand editionWeb27 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 … cso number hp

"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 k -Metric Dimension of Corona Product Graphs - Springer

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 ... 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 ...

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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 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 …

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 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 …

Web31 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 … 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 …

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 ...

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 … ealgreens mini clinc fee wax removalWeb15 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 ... ealfwinWeb31 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. ealh 1508Web1 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 … cso nst beta 3WebThe 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 … cso obesite strasbourgWeb20 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 … csonty dutyWebThe 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. cso-nst2.1