The local strong metric dimension in the join of graphs

Amalia, Rica and Firdausiyah, Firdausiyah and Yulianto, Tony and Faisol, Faisol and Kuzairi, Kuzairi (2022) The local strong metric dimension in the join of graphs. Journal of Physics: Conference Series, 2157 (1).

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Abstract

Let G be a connected graph. A vertex w is said to strongly resolve a pair u, ν of vertices of G if there exists some shortest u − w path containing ν or some shortest ν − w path containing u. A set W of vertices is a local strong resolving set for G if every pair of adjacent vertices of G is strongly resolved by some vertex of W. The smallest cardinality of a local strong resolving set for G is called the local strong metric dimension of G. In this paper we studied the local strong metric dimension in the join of graphs. We use the path, cycle, complete, and star graphs in this studies.

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