Locating domination number of m-shadowing of graphs
Dafik Dafik, Ika Hesti Agustin, Ermita Rizki Albirri, Ridho Alfarisi, Rafiantika Megahnia Prihandini · Journal of Physics Conference Series · 2018
Let G = ( V, E ) be a connected, undirected and simple graph. We define a set D as a dominating set if for every vertex is adjacent to some vertex . The domination number is the minimum cardinality of dominating set. A vertex set D in graph G = ( V, E ) is called locating dominating set if for every pair of different vertex u and v in V ( G ) − D which occupies where N ( u ) is adjacency vertex set of u. The minimal cardinality of locating domination number is denoted by . We present about the locating dominating set of m -shadowing graph. Let G be simple and connected graph. The m -shadow graph D m ( G ) of a connected graph G is constructed by taking m copies of G , say G 1 , G 2 , ..., G m , then join each vertex u in G i to the neighbors of the corresponding vertex v in G j , 1 ≤ i , j ≤ m .