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