Affiliations: [a] Departament d’Enginyeria Informàtica i Matemàtiques, Av. Països Catalans 26, 43007 Tarragona, Spain. [email protected] | [b] Departamento de Matemáticas, Escuela Politécnica Superior de Algeciras, Universidad de Cádiz, Av. Ramón Puyol s/n, 11202 Algeciras, Spain. [email protected] | [c] Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain. [email protected]
Note: [*] Address for correspondence: Departament d’Enginyeria Informática i Matemátiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain.
Abstract: A vertex w of a connected graph G strongly resolves two vertices u, v ∈ 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.
