Graphs with three distinct distance eigenvalues

DOI10.1016/J.AMC.2023.127848arXiv2112.10375MaRDI QIDQ6386154

Publication date: 20 December 2021

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.

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

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