On the Cayleyness of bipartite Kneser graphs

For any given n,k \in \mathbb{N} with ۲k < n, the bipartite\ Kneser \ graph H(n, k) is defined as the graph whose vertex set is the family of k-subsets and (n-k)-subsets of [n] = \{۱, ۲,\dots, n\}, in whichany two vertices are adjacent if and only if one of them is a subset of the other.In this paper, we study some algebraic properties of the bipartite Kneser graph H(n, k). In particular, we determine the values of n,k, for which the bipartite Knesergraph H(n,k) is a Cayley graph.

Keywords:

bipartite Kneser graph , vertex-transitive graph , automorphism