On the locating domination number of corona product
Risan Nur Santi, Ika Hesti Agustin, Dafik Dafik, Ridho Alfarisi · Journal of Physics Conference Series · 2018
Let G = ( V ( G ), E ( G ) be a connected graph and v ∊ V ( G ). A dominating set for a graph G = ( V , E ) is a subset D of V such that every vertex not in D is adjacent to at least one member of D . The domination number γ( G ) is the number of vertices in a smallest dominating set for G . Vertex set S in graph G = ( V, E ) is a locating dominating set if for each pair of distinct vertices u and v in V ( G ) − S we have , and , that is each vertex outside of S is adjacent to a distinct, nonempty subset of the elements of S . In this paper, we characterize the locating dominating sets in the corona product of graphs namely path, cycle, star, wheel, and fan graph.