Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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REMARKS ON THE INNER POWER OF GRAPHS

  • JAFARI, S. (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan) ;
  • ASHRAFI, A.R. (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan) ;
  • FATH-TABAR, G.H. (University of Kashan) ;
  • TAVAKOLI, Mostafa (Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad)
  • Received : 2016.02.05
  • Accepted : 2016.11.17
  • Published : 2017.01.30
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Abstract

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 $G^{(2)}$.

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References

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