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The square of a graph G= (V, E) is the graph G2 with the same vertex set as G and every two vertices u, v ϵ V are adjacent in G2 if and only if they are adjacent in G by a path of length one or two. Throughout this paper an attempt has been done to analyse the global domination of squares of certain graphs. We considered some connected graphs like paths, cycles, wheel graphs, complete tripartite, windmill graphs and some tree graphs. We characterised the global domination number of squares of a graph. We obtained a relationship between the global domination number of the square of some graphs and the domination number of the given graph. We also obtained the global domination number of squares of certain graphs.
AMS Subject Classification: 05C69