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 ... 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 ...

The k -Metric Dimension of Corona Product Graphs - Springer

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 … 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 … how do you make a basketball hoop

(PDF) The -Size Edge Metric Dimension of Graphs - ResearchGate

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. 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. 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 how do you make a barn in little alchemy 2

[1809.08900] Edge metric dimension of some graph operations

The effect of vertex and edge deletion on the edge metric …

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 … 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 … phone cases for samsung galaxy z fold3WebAn 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 ... how do you make a beacon work

"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 … " - On the edge metric dimension of graphs

On the edge metric dimension of graphs

(PDF) The -Size Edge Metric Dimension of Graphs - ResearchGate

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 … 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 …

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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 … 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 …

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 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 …

Web1 de dez. de 2014 · 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 … 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 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 … phone cases for samsung s21 ultraWeb17 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 … phone cases for schokWeb23 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 … phone cases for samsung z fold 4Web21 de dez. de 2016 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … phone cases for telstra essential smart 2.1Web1 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 … phone cases for schok sv55Web1 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 … how do you make a bed in minecraftWeb1 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 … phone cases for small phones