Secure metric dimension of new classes of graphs

The metric representation of a vertex v of a graph G is a finite vector representing distances of v with respect to vertices of some ordered subset (Formula Presented). If no suitable subset of S provides separate representations for each vertex of V(G), then the set S is referred to as a minimal resolving set. The metric dimension of G is the cardinality of the smallest (with respect to its cardinality) minimal resolving set. A resolving set S is secure if for any (Formula Presented), there exists (Formula Presented) such that (Formula Presented) is a resolving set. For various classes of graphs, the value of the secure resolving number is determined and defined. The secure metric dimension of the graph classes is being studied in this work. The results show that different graph families have different metric dimensions.