This article introduces a new family of Cayley graphs, called k -degree Cayley graphs, for building interconnection networks. The k -degree Cayley graph possesses many valuable topological properties, such as regularity with degree k , logarithmic diameter, and maximal fault tolerance. We present an optimal shortest path routing algorithm for the k -degree Cayley graph. Cycleembedding and clique-embedding are also discussed.

This paper introduces a new family of Cayley graphs, named the k-valent graphs, for building interconnection networks. It includes the trivalent Cayley graphs (Vadapalli and Srimani, 1995) as a subclass. These new graphs are shown to be regular with the node-degree k, to have logarithmic diameter subject to the number of nodes, and to be k-connected as well as maximally fault tolerant. We also propose a shortest path routing algorithm and investigate some algebraic properties like cycles or cliques embedding.