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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 4682527, 9 pages
http://dx.doi.org/10.1155/2016/4682527
Research Article

Further Results on Resistance Distance and Kirchhoff Index in Electric Networks

1Department of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
2Department of Public Courses, Anhui Xinhua University, Hefei 230088, China
3Research Center for Complex Systems and Network Science, Department of Mathematics, Southeast University, Nanjing 210096, China

Received 11 September 2015; Revised 31 December 2015; Accepted 6 January 2016

Academic Editor: Juan R. Torregrosa

Copyright © 2016 Qun Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.