On the edge metric dimension of graphs
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 … 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 …
On the edge metric dimension of graphs
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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 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 ... 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 …
Web1 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 … 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: …
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 … Web28 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
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 …
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 … sharefile for outlook not workingWeb23 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 … poop not coming out all the wayWeb8 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 ... sharefile for outlook downloadWeb21 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 … sharefile filepart upload failedWeb8 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 … sharefile for windows 10Web27 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 poop object showWeb21 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. sharefile for outlook plugin