The local metric dimension of amalgamation of graphs - Fitriani, Dinny; Saputro, Suhadi Wido (Electronic Journal of Graph Theory and Applications (EJGTA), 2024)
For any two adjacent vertices u and v in graph G, a set of vertices W locally resolves a graph G if the distance of u and v to some elements of W are distinct. The local metric dimension of G is the minimum cardinality of local resolving sets of G. For n ∈ N and i ∈ {1, 2, …, n}, let Hi be a simple connected graph containing a connected subgraph J. Let H = {H1, H2, …, Hn} be a finite collection of simple connected graphs. The subgraph-amalgamation of H = {H1, H2, …, Hn}, denoted by Subgraph − Amal{H; J}, is a graph obtained by identifying all elements of H in J. The subgraph J is called as a terminal subgraph of H. In this paper, we determine general bounds of the local metric dimension of subgraph-amalgamation graphs for any connected terminal subgraphs. We also determine the local metric dimension of Subgraph − Amal{H; J} for J is either K1 or P2.