A new class of transitive graphs

Let nn and kk be integers with n≥k≥0n≥k≥0. This paper presents a new class of graphs H(n,k)H(n,k), which contains hypercubes and some well-known graphs, such as Johnson graphs, Kneser graphs and Petersen graph, as its subgraphs. The authors present some results of algebraic and topological properties of H(n,k)H(n,k). For example, H(n,k)H(n,k) is a Cayley graph, the automorphism group of H(n,k)H(n,k) contains a subgroup of order 2nn!2nn! and H(n,k)H(n,k) has a maximal connectivity nk and is hamiltonian if kk is odd; it consists of two isomorphic connected components if kk is even. Moreover, the diameter of H(n,k)H(n,k) is determined if kk is odd.