Resistance distances and the Kirchhoff index in Cayley graphs |
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Authors: | Xing Gao Yanfeng LuoWenwen Liu |
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Institution: | Department of Mathematics, Lanzhou University, Lanzhou, 730000, PR China |
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Abstract: | In this paper, closed-form formulae for the Kirchhoff index and resistance distances of the Cayley graphs over finite abelian groups are derived in terms of Laplacian eigenvalues and eigenvectors, respectively. In particular, formulae for the Kirchhoff index of the hexagonal torus network, the multidimensional torus and the t-dimensional cube are given, respectively. Formulae for the Kirchhoff index and resistance distances of the complete multipartite graph are obtained. |
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Keywords: | Cayley graph Kirchhoff index Resistance distance Laplacian eigenvalue |
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