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Kirchhoff index in line,subdivision and total graphs of a regular graph
Authors:Xing Gao  Yanfeng Luo  Wenwen Liu
Institution:Department of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, PR China
Abstract:Let G be a connected regular graph and l(G), s(G), t(G) the line, subdivision, total graphs of G, respectively. In this paper, we derive formulae and lower bounds of the Kirchhoff index of l(G), s(G) and t(G), respectively. In particular, we give special formulae for the Kirchhoff index of l(G), s(G) and t(G), where G is a complete graph Kn, a regular complete bipartite graph Kn,n and a cycle Cn.
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