On the Diameter of Wenger Graphs |
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Authors: | Raymond Viglione |
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Institution: | (1) Department of Mathematics, Kean University, Union, NJ 07083, USA |
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Abstract: | Let q be a prime power,
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
, 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. |
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Keywords: | Wenger graph Diameter |
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