Bipartite Domination in Some Classes of Graphs

For a nontrivial connected graphG, a non-empty setS⊆V(G) is a bipartite dominating set of graphG, ifthe subgraphG[S] induced bySis bipartite and for every vertex not inSis dominated by any vertex inS.The bipartite domination number denoted byγbip(G) of graphGis the minimum cardinality of a bipartitedominating setG. In this paper, we determine the exact bipartite domination number of path graph andcycle graph via congruence modulo. Moreover, this study generates the possible exact values of the bipartitedomination number of the complete graph, complete bipartite graph, join graph, fan graph and wheel graph.