Further Results on Resistance Distance and Kirchhoff Index in Electric Networks

Qun Liu, Jia-Bao Liu and Jinde Cao

Discrete Dynamics in Nature and Society, 2016, vol. 2016, 1-9

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 be the graph obtained from by inserting a new vertex into every edge of and by joining by edges those pairs of these new vertices which lie on adjacent edges of . The set of such new vertices is denoted by . The -vertex corona of and , denoted by , is the graph obtained from vertex disjoint and copies of by joining the th vertex of to every vertex in the th copy of . The -edge corona of and , denoted by , is the graph obtained from vertex disjoint and copies of by joining the th vertex of to every vertex in the th copy of . The objective of the present work is to obtain the resistance distance and Kirchhoff index for composite networks such as -vertex corona and -edge corona networks.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:4682527

DOI: 10.1155/2016/4682527

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