On the edge metric dimension of graphs
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 … 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 ...
On the edge metric dimension of graphs
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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 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 …
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 ... 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 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 … 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 …
Web1 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 …
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 … immersion blender with pan guardWeb31 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 … list of south australian schoolsWeb20 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 … list of southern hemisphere tornado outbreaksWeb1 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 … immersion blender with metal gearsWeb15 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 ... immersion blender whisk attachment usesWeb19 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) = … immersion blender with oatmealWeb1 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 ... list of southern university alumni wikipedia