• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.25-32
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• 2017

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 $k^{th}$ 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 the first and second Zagreb indices and coindices of $G^{(2)}$.