Bipartite Domination in Some Classes of Graphs

For a nontrivial connected graph G, a non-empty set S \(\subseteq\) V (G) is a bipartite dominating set of graph G, if the subgraph G[S] induced by S is bipartite and for every vertex not in S is dominated by any vertex in S. The bipartite domination number denoted by \(\gamma\)bip(G) of graph G is the minimum cardinality of a bipartite dominating set G. In this paper, we determine the exact bipartite domination number of path graph and cycle graph via congruence modulo. Moreover, this study generates the possible exact values of the bipartite domination number of the complete graph, complete bipartite graph, join graph, fan graph and wheel graph.