On locating independent domination number of amalgamation graphs
Dwi Agustin Retnowardani, Dafik Dafik, Ika Hesti Agustin, Elsa Yuli Kurniawati · Journal of Physics Conference Series · 2017
An independent set or stable set is a set of vertices in a graph in which no two of vertices are adjacent. A set D of vertices of graph G is called a dominating set if every vertex u V ( G ) — D is adjacent to some vertex v D . A set S of vertices in a graph G is an independent dominating set of G if D is an independent set and every vertex not in D is adjacent to a vertex in D . By locating independent dominating set of graph G, we mean that an independent dominating set D of G with the additional properties that for u , v ( V — D ) satisfies N ( u ) ∩ D ≠ N ( v ) ∩ D . A minimum locating independent dominating set is a locating independent dominating set of smallest possible size for a given graph G. This size is called the locating independent dominating number of G and denoted γ Li ( G ). In this paper, we analyze the locating independent domination number of graph operations.