#### Title

### On the diameter of Wenger graphs

#### Document Type

Article

#### Publication Date

11-1-2008

#### Abstract

Let q be a prime power, q the field of q elements, and n≥1 a positive integer. The Wenger graph W n (q) is defined as follows: the vertex set of W n (q) is the union of two copies P and L of (n+1)-dimensional vector spaces over script F signq, with two vertices (p 1,p 2,p n+1) P and [l 1,l 2,l n+1] L being adjacent if and only if l i +p i =p 1 l i-1 for 2≤i≤n+1. Graphs W n (q) have several interesting properties. In particular, it is known that when connected, their diameter is at most 2n+2. In this note we prove that the diameter of connected Wenger graphs is 2n+2 under the assumption that 1≤n≤q-1. © 2008 Springer Science+Business Media B.V.

#### Publication Title

Acta Applicandae Mathematicae

#### First Page Number

173

#### Last Page Number

176

#### DOI

10.1007/s10440-008-9249-8

#### Recommended Citation

Viglione, Raymond, "On the diameter of Wenger graphs" (2008). *Kean Publications*. 2455.

https://digitalcommons.kean.edu/keanpublications/2455