paper

Graphs with three distinct distance eigenvalues

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 ${C_{3}, C_{4}}$ -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.

17 pages