# On jumped Wenger graphs

## TL;DR

This paper introduces a new class of bipartite graphs called jumped Wenger graphs, providing bounds on their diameter and girth, and explicitly calculating diameters for specific parameter cases, advancing graph theory understanding.

## Contribution

It defines jumped Wenger graphs, establishes their diameter and girth bounds, and computes exact diameters for particular parameter configurations, enriching the study of bipartite graphs.

## Key findings

- Determined tight upper bounds for diameter and girth.
- Calculated exact diameters for specific jumped Wenger graphs.
- Established the relationship between jumped Wenger graphs and 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 $i, j$, $1\leq i <j \leq m+2$, 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.