On jumped Wenger graphs

Abstract

In this paper we introduce a new infinite class of bipartite graphs, called jumped Wenger graphs, which are closely related to Wenger graphs. An tight upper bound of the diameter and the exact girth of a jumped Wenger graph $J_m(q,i,j)$ for integers $i,j$, $1\le i<j\le m+2$, are determined. In particular, the exact diameter of the jumped Wenger graph $J_m(q,i,j)$ if $(i,j)=(m,m+2),(m+1,m+2)$ or $(m,m+1)$ is also obtained.