Remarks on the Inner Power of Graphs

چکیده مقاله

Let G be a graph and k is a positive integer. Hammack and Livesay in [The inner power of a graph, Ars Math. Contemp., 3 (2010), no. 2, 193{199] introduced a new graph operation G(k), called the kth inner power of G. In this paper, it is proved that if G is bipartite then G(2) has exactly three components such that one of them is bipartite and two others are isomorphic. As a consequence the edge frustration index of G(2) is computed based on the same values as for the original graph G. We also compute therst and second Zagreb indices and coindices of G(2).