Graphs with three distinct distance eigenvalues

2021/12/20 by Zhang, Yuke, Lin, Huiqiu · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.10375

Abstract

In this paper, some special distance spectral properties of graphs are considered. Concretely, we recursively construct an infinite family of trees with distance eigenvalue -1, and determine all \C₃,C₄\-free connected graphs with three distinct distance eigenvalues of which the smallest one is equal to -3, which partially answers a problem posed by Koolen, Hayat and Iqbal [Linear Algebra Appl. 505 (2016) 97--108]. Furthermore, we characterize all trees with three distinct distance eigenvalues.

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• Distance spectral radius for a graph to be k-critical with respect to [1,b]-odd factor

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