on the distance transitivity of the bipartite kneser graphs

In this paper, we study a family of graphs related to johnson graphs, known as bipartite kneser graphs. let n and k be integers such that n>k 1≥. we denote by h(n, k) the bipartite kneser graph, whose vertex set consists of all k-subsets and (n - k)-subsets of the set [n] = {1, 2, ..., n}, where two vertices are adjacent if and only if one is a subset of the other. mirafzal (s. m. mirafzal, the automorphism group of the bipartite kneser graph, proc. indian acad. sci. (math. sci.), (2019) 129 (34), proved that the automorphism group of the bipartite kneser graph h(n, k) is isomorphic to sym ([n])×z2. in this paper, we investigate the distance-transitivity and the diameter of the bipartite kneser graphs. it is known that h(n, k) is distance-transitive precisely when k=1 or n=2k+1. in this work, we provide new structural proofs of these cases directly within the bipartite kneser framework, and we determine the diameter of h(n, k) for various ranges of n and k.