On the distance in some bipartite graphs $L_{k,n}$

Abstract

The paper presents some bipartite graph $L_{k,n}$, so called $(k,n)$-level graph, that arise by taking $k$-th and $(n-k)$-th levels of $n$-dimensional Boolean algebra. Two results are establised: (1) precise description of a distance (a shotest path) beteen arbitrary vertices and (2) solution of the problem how many vertices may be reached in $i$ steps starting from some intial point.