Metric dimension of generalized wheels

Q2 Mathematics

Arab Journal of Mathematical Sciences Pub Date : 2019-07-01 DOI:10.1016/j.ajmsc.2019.04.002

Badekara Sooryanarayana , Shreedhar Kunikullaya , Narahari Narasimha Swamy

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引用次数: 5

Abstract

In a graph $G$ , a vertex $w \in V (G)$ resolves a pair of vertices $u, v \in V (G)$ if $d (u, w) \neq d (v, w)$ . A resolving set of $G$ is a set of vertices $S$ such that every pair of distinct vertices in $V (G)$ is resolved by some vertex in $S$ . The minimum cardinality among all the resolving sets of $G$ is called the metric dimension of $G$ , denoted by $β (G)$ . The metric dimension of a wheel has been obtained in an earlier paper (Shanmukha et al., 2002). In this paper, the metric dimension of the family of generalized wheels is obtained. Further, few properties of the metric dimension of the corona product of graphs have been discussed and some relations between the metric dimension of a graph and its generalized corona product are established.

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广义车轮的公制尺寸

在图G中，如果d(u,w)≠d(V,w)，则顶点w∈V(G)可以解析一对顶点u, V∈V(G)。G的解析集是顶点S的集合，使得V(G)中的每一对不同的顶点都能被S中的某个顶点解析。G的所有解析集的最小基数称为G的度量维数，用β(G)表示。车轮的公制尺寸已在较早的论文中获得(Shanmukha et al.， 2002)。本文给出了广义车轮族的度量维数。进一步讨论了图的电晕积的度量维数的几个性质，建立了图的度量维数与其广义电晕积之间的一些关系。

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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