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.