On the strong metric dimension of Cartesian sum graphs

Abstract

A vertex $w$ of a connected graph $G$ strongly resolves two vertices $u,v\in V(G)$, if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A set $S$ of vertices is a strong metric generator for $G$ if every pair of vertices of $G$ is strongly resolved by some vertex of $S$. The smallest cardinality of a strong metric generator for $G$ is called the strong metric dimension of $G$. In this paper we obtain several tight bounds or closed formulae for the strong metric dimension of the Cartesian sum of graphs in terms of the strong metric dimension, clique number or twins-free clique number of its factor graphs.

arXiv admin note: text overlap with arXiv:1402.2663

References in corpus (1)

• On the strong metric dimension of corona product graphs and join graphs

Cited by in corpus (3)

• Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results
• Strong resolving graphs: the realization and the characterization problems
• On the Strong Metric Dimension of directed co-graphs