On the edge metric dimension of graphs

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Web10 de abr. de 2024 · Signal Variation Metrics and Graph Fourier Transforms for Directed Graphs. Laura Shimabukuro, Antonio Ortega. Published 10 April 2024. Mathematics, Computer Science. In this paper we consider the problem of constructing graph Fourier transforms (GFTs) for directed graphs (digraphs), with a focus on developing multiple … 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 …

Uniquely identifying the edges of a graph: The edge …

Web31 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 … 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 … how many 3d fillings does a cube have

(PDF) Edge metric dimension of graphs - ResearchGate

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 … 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 ... 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 … high mover

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On the Edge Metric Dimension of Certain Polyphenyl Chains

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 … 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 … how many 3d electrons does a mn2+ ion haveWeb10 de abr. de 2024 · Signal Variation Metrics and Graph Fourier Transforms for Directed Graphs. Laura Shimabukuro, Antonio Ortega. Published 10 April 2024. Mathematics, … how many 3d electrons are in an atom of zn

"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. " - 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 …

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 … 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 ...

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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. 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 …

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 ... 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 …

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 ...

Web3 de jan. de 2024 · DOI: 10.1007/s10878-021-00838-7 Corpus ID: 245654396; The effect of vertex and edge deletion on the edge metric dimension of graphs @article{Wei2024TheEO, title={The effect of vertex and edge deletion on the edge metric dimension of graphs}, author={Meiqin Wei and Jun Yue and Lily Chen}, …

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: … how many 39 steps filmsWeb23 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 … how many 3d electrons are in an atom of feWeb18 de dez. de 2024 · DOI: 10.1155/2024/3855172 Corpus ID: 245338040; On the Edge Metric Dimension of Certain Polyphenyl Chains @article{Ahsan2024OnTE, title={On the Edge Metric Dimension of Certain Polyphenyl Chains}, author={Muhammad Ahsan and Zohaib Zahid and Dalal Awadh Alrowaili and Aiyared Iampan and Imran Siddique and … how many 3\u0027s in this picture answerWeb21 de dez. de 2016 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … how many 3\u0027s has ben simmons made in the nbaWebThe 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. how many 3d shapes are thereWeb6 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 … how many 3d printed homes have been builtWeb27 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 high mower seeds