A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Honeycomb Networks: Topological Properties and Communication Algorithms
IEEE Transactions on Parallel and Distributed Systems
A family of Cayley graphs on the hexavalent grid
Discrete Applied Mathematics
Uniform emulations of Cartesian-product and Cayley graphs
Discrete Applied Mathematics
IEEE Transactions on Parallel and Distributed Systems
Further mathematical properties of Cayley digraphs applied to hexagonal and honeycomb meshes
Discrete Applied Mathematics
Short containers in Cayley graphs
Discrete Applied Mathematics
A recursion formula for resistance distances and its applications
Discrete Applied Mathematics
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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.