On the Kirchhoff index of some toroidal lattices |
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Authors: | Luzhen Ye |
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Institution: | 1. School of Sciences , Jimei University , Xiamen 361021, China lzye555@sina.com |
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Abstract: | The resistance distance is a novel distance function on a graph proposed by Klein and Randi? D.J. Klein and M. Randi?, Resistance distance, J. Math. Chem. 12 (1993), pp. 81–85]. The Kirchhoff index of a graph G is defined as the sum of resistance distances between all pairs of vertices of G. In this article, based on the result by Gutman and Mohar I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996), pp. 982–985], we compute the Kirchhoff index of the square, 8.8.4, hexagonal and triangular lattices, respectively. |
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Keywords: | Kirchhoff index lattice Laplacian eigenvalue |
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