(untitled) (Contemporary Mathematics, 2025)
This paper investigates the independence number of various graph classes. The independence number of a graph G, denoted by α(G), is the size of the largest subset of vertices in G such that no two vertices in the subset are adjacent. In this paper, we introduce the independent metric dimension (idim) of some graphs such as comb graph, double comet graph, arrow graph and double arrow graph. In particular, we derive the explicit formulas for the double comb graph, spider graph, fire cracker graph and tadpole graph.