A new class of transitive graphs

Let n and k be integers with n ≥ k ≥ 0 . This paper presents a new class of graphs 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 ) . For example, H ( n , k ) is a Cayley graph, the automorphism group of H ( n , k ) contains a subgroup of order 2 n n ! and H ( n , k ) has a maximal connectivity n k and is hamiltonian if k is odd; it consists of two isomorphic connected components if k is even. Moreover, the diameter of H ( n , k ) is determined if k is odd.