The graphs with exactly two distance eigenvalues different from \(-1\) and
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- 作者：Lu Lu ; Qiongxiang Huang ; Xueyi Huang
- 关键词：Distance eigenvalue ; Distance equitable partition ; Friendship graph ; Distance spectral characterization
- 刊名：Journal of Algebraic Combinatorics
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：45
- 期：2
- 页码：629-647
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Combinatorics; Convex and Discrete Geometry; Order, Lattices, Ordered Algebraic Structures; Computer Science, general; Group Theory and Generalizations;
- 出版者：Springer US
- ISSN：1572-9192
- 卷排序：45
文摘
In this paper, we completely characterize the graphs with third largest distance eigenvalue at most \(-1\) and smallest distance eigenvalue at least \(-3\). In particular, we determine all graphs whose distance matrices have exactly two eigenvalues (counting multiplicity) different from \(-1\) and \(-3\). It turns out that such graphs consist of three infinite classes, and all of them are determined by their distance spectra. We also show that the friendship graph is determined by its distance spectrum.