1. On the Kirchhoff index of some toroidal lattices.
- Author
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Ye, Luzhen
- Subjects
- *
KIRCHHOFF'S theory of diffraction , *LATTICE theory , *GRAPH theory , *PATHS & cycles in graph theory , *LAPLACIAN operator , *EIGENVALUES , *MATHEMATICAL functions - Abstract
The resistance distance is a novel distance function on a graph proposed by Klein and Randic [D.J. Klein and M. Randic, 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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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