Vertex resolvability of convex polytopes with n-paths of length p

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
Sahil Sharma, V. K. Bhat
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引用次数: 1

Abstract

Let be a simple, connected, and undirected graph. The distance between two vertices denoted by , is the length of the shortest path connecting u and v. A subset of vertices is said to be a resolving set for G if for any two distinct vertices V, there exist a vertex such that . A minimal resolving set is called a metric basis, and the cardinality of the basis set is called the metric dimension of G, denoted by . In this article, we find the metric dimension for two infinite families of plane graphs and , where is obtained by the combination of copies of bipartite graphs , and is obtained by the combination of double antiprism graph with antiprism graph and then adding n-paths of length p.
长度为p的n条路径凸多面体的顶点可分辨性
设一个简单的,连通的,无向图。两个顶点之间的距离用表示,是连接u和V的最短路径的长度。如果对于任意两个不同的顶点V,存在这样一个顶点,则顶点的子集被称为G的解析集。最小解析集称为度量基,基集的基数称为G的度量维数,表示为。本文给出了两个无限族平面图的度量维数,其中度量维数是由二部图的拷贝组合得到的,度量维数是由双反棱镜图与反棱镜图组合,然后加上长度为p的n条路径得到的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
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