On the Spectrum of Wenger Graphs

2014/02/14 by Sebastian M. Cioabă, Cioabă, Sebastian M., Felix Lazebnik +3
Computer Science · Mathematics · #05C50 #15A18 #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1402.3341

openalex publication_date 2014/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q=p^e, where p is a prime and e≥ 1 is an integer. For m≥ 1, let P and L be two copies of the (m+1)-dimensional vector spaces over the finite field \mathbbF_q. Consider the bipartite graph W_m(q) with partite sets P and L defined as follows: a point (p)=(p₁,p₂,…,p_m+1)∈ P is adjacent to a line [l]=[l₁,l₂,…,l_m+1]∈ L if and only if the following m equalities hold: l_i+1 + p_i+1=l_ip₁ for i=1,…, m. We call the graphs W_m(q) Wenger graphs. In this paper, we determine all distinct eigenvalues of the adjacency matrix of W_m(q) and their multiplicities. We also survey results on Wenger graphs.

Related

• Linearized Wenger graphs
• Automorphism Group of the Spectral Incidence Graph over Finite Fields
• The graphs with all but two eigenvalues equal to ± 1
• The spectrum of a class of graphs derived from Grassmann graphs
• The signed graphs with two eigenvalues unequal to ± 1