Elsevier

Discrete Mathematics

Volume 340, Issue 5, May 2017, Pages 1050-1053
Discrete Mathematics

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A note on the spectrum of linearized Wenger graphs

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Abstract

Let Fq be a finite field of order q=pe, where p is a positive prime. For m1, let P and L be two copies of Fqm+1. To each m-tuple g=(g2,,gm+1) of polynomials in Fq[x,y], we consider the bipartite graph Wq(g). The vertex set V of Wq(g) is PL. The edge set E of Wq(g) consists of (p,l)P×L satisfying p2+l2=g2(p1,l1),p3+l3=g3(p1,l1),,pm+1+lm+1=gm+1(p1,l1),where p=(p1,p2,,pm+1)P and l=(l1,l2,,lm+1)L. Wq(g) is called linearized Wenger graph when g=(xy,xpy,,xpm1y). In this paper, we determine the eigenvalues of linearized Wenger graph and their multiplicities in the case of m<e, which is an open problem put forward by Cao et al. (2015).

Keywords

Eigenvalues of graphs
Graph spectrum
Linearized Wenger graph

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