On the diameter of Wenger graphs

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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.

Original languageEnglish
Pages (from-to)173-176
Number of pages4
JournalActa Applicandae Mathematicae
Volume104
Issue number2
DOIs
StatePublished - Nov 2008

Keywords

  • Diameter
  • Wenger graph

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