Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656869 | Journal of Combinatorial Theory, Series B | 2014 | 8 Pages |
Abstract
Let q=peq=pe, where p is a prime and e⩾1e⩾1 is an integer. For m⩾1m⩾1, let P and L be two copies of the (m+1)(m+1)-dimensional vector spaces over the finite field FqFq. Consider the bipartite graph Wm(q)Wm(q) with partite sets P and L defined as follows: a point (p)=(p1,p2,…,pm+1)∈P(p)=(p1,p2,…,pm+1)∈P is adjacent to a line [l]=[l1,l2,…,lm+1]∈L[l]=[l1,l2,…,lm+1]∈L if and only if the following m equalities hold: li+1+pi+1=lip1li+1+pi+1=lip1 for i=1,…,mi=1,…,m. We call the graphs Wm(q)Wm(q) Wenger graphs. In this paper, we determine all distinct eigenvalues of the adjacency matrix of Wm(q)Wm(q) and their multiplicities. We also survey results on Wenger graphs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Sebastian M. Cioabă, Felix Lazebnik, Weiqiang Li,