Abstract: 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.


Keywords: Domination, Bipartite dominating set, Bipartite domination number, Topological indices, Bipartite domination topological indices.

AMS subject classification: 05C69, 05C76, 68R10.

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