On the LIDS of corona product of graphs

Let G = (V, E) be a simple, undirected, and nontrivial graph. An independent set is a set of vertices in a graph in which no two of vertices are adjacent. A dominating set of a graph G is a set D of vertices of G such that every vertex not in S is adjacent to a vertex in D. An independent dominating set in a graph is a set that is both dominating and independent. Equivalently, an independent dominating set is a maximal independent set. Locating independent dominating set of graph G is independent dominating set with the additional characteristics that for u, v ∈ (V(G) − D) satisfies N(u) ∩ D ≠ N(v) ∩ D. γLi(G) is the minimum cardinality of locating dominating set we call Locating domination number. In this paper, we analyze the locating independent domination number of corona product of path, cycle, gear, wheel, and ladder graph. We also analyze whether locating independent domination number of corona product depends on its constituent graphs.