On the edge metric dimension of graphs

Author: kqde

August undefined, 2024

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. Web14 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 …

Metric Dimension on Path-Related Graphs - Hindawi

Web10 de abr. de 2024 · Signal Variation Metrics and Graph Fourier Transforms for Directed Graphs. Laura Shimabukuro, Antonio Ortega. Published 10 April 2024. Mathematics, … shutterfly christmas card

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

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 ... 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. 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. the paintings three

The dominant edge metric dimension of graphs - ResearchGate

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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 ... 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 … shutterfly christmas cards 2019Web1 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 … the paintings of vincent van gogh

"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. " - On the edge metric dimension of graphs

On the edge metric dimension of graphs

[2010.11023] On the robustness of the metric dimension of grid …

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 … 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 …

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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 … 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 …

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 ... 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 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 … Web11 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: …

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 …

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 … shutterfly cell phone casesWeb15 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 … the painting spotWeb19 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) = … shutterfly christmas cards 2018Web31 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 … the painting the angelusWebThe 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 … the painting was beautiful. i stood thereWeb31 de dez. de 2024 · The edge metric dimension of graph is the minimum cardinality of edge resolving set, say , and is denoted as . An edge metric generator for of … shutterfly christmas cards 2022Web23 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 … shutterfly christmas cards 2021