On the edge metric dimension of graphs
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 … 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 …
On the edge metric dimension of graphs
Did you know?
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 ... 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 …
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 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 …
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 · 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 …
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 …
Web18 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 do you sleep mccartneyWeb3 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}, … how do you sleep most peopleWeb28 de jan. de 2024 · [4] V. Filipović, A. Kartelj and J. Kratica, Edge metric dimension of some generalized Petersen graphs, Results Math. 74 (2024) Article 182. 10.1007/s00025-019-1105-9 Search in Google Scholar [5] F. Harary and R.A. Melter, On the metric dimension of a graph, Ars Combin. 2 (1976) 191–195. Search in Google Scholar how do you sleep on an amtrak trainWebThe 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 do you sleep on your periodWeb1 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 ... how do you sleep meaningWebThe 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 ... phone selling shops near meWebThe 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 … phone selling in jamaica