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Further Results on Resistance Distance and Kirchhoff Index in Electric Networks

Author

Listed:
  • Qun Liu
  • Jia-Bao Liu
  • Jinde Cao

Abstract

In electric circuit theory, it is of great interest to compute the effective resistance between any pairs of vertices of a network, as well as the Kirchhoff index. Let Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. The set of such new vertices is denoted by I(G). The Q‐vertex corona of G1 and G2, denoted by G1⊙QG2, is the graph obtained from vertex disjoint Q(G1) and |V(G1)| copies of G2 by joining the ith vertex of V(G1) to every vertex in the ith copy of G2. The Q‐edge corona of G1 and G2, denoted by G1⊖QG2, is the graph obtained from vertex disjoint Q(G1) and |I(G1)| copies of G2 by joining the ith vertex of I(G1) to every vertex in the ith copy of G2. The objective of the present work is to obtain the resistance distance and Kirchhoff index for composite networks such as Q‐vertex corona and Q‐edge corona networks.

Suggested Citation

  • Qun Liu & Jia-Bao Liu & Jinde Cao, 2016. "Further Results on Resistance Distance and Kirchhoff Index in Electric Networks," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:4682527
    DOI: 10.1155/2016/4682527
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    References listed on IDEAS

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    1. R. B. Bapat & Somit Gupta, 2010. "Resistance distance in wheels and fans," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 1-13, February.
    2. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.
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