TY - JOUR
T1 - On the diameter of Wenger graphs
AU - Viglione, Raymond
PY - 2008/11
Y1 - 2008/11
N2 - 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.
AB - 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.
KW - Diameter
KW - Wenger graph
UR - http://www.scopus.com/inward/record.url?scp=52949150792&partnerID=8YFLogxK
U2 - 10.1007/s10440-008-9249-8
DO - 10.1007/s10440-008-9249-8
M3 - Article
AN - SCOPUS:52949150792
SN - 0167-8019
VL - 104
SP - 173
EP - 176
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
IS - 2
ER -