Graphs with at most three distance eigenvalues different from -1 and -2

2017/08/26 by Xueyi Huang, Qiongxiang Huang, Huang, Xueyi +3
Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50

paper · pdf · doi:10.48550/arxiv.1708.07979

17 pages, 3 figures

arxiv created 2017/08/26 · arxiv updated 2017/08/29

Abstract

Let G be a connected graph on n vertices, and let D(G) be the distance matrix of G. Let ∂₁(G)≥∂₂(G)≥⋯≥∂_n(G) denote the eigenvalues of D(G). In this paper, we characterize all connected graphs with ∂₃(G)≤ -1 and ∂_n-1(G)≥ -2. By the way, we determine all connected graphs with at most three distance eigenvalues different from -1 and -2.

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