ON BIPARTITE DOMINATION TOPOLOGICAL INDICES OF SOME GRAPHS

For a nontrivial connected graph G, a nonempty set S⊆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. In this paper, we define a new bipartite dominating degree (bdd) of each vertex x∈V(G), called bipartite domination degree of x and denoted by dbγ(G). Also, we establish exact value for the bdd zagreb indices of some class of graph.