1. Signed graphs with exactly two distinct main eigenvalues.
- Author
-
Du, Zenan, You, Lihua, Liu, Hechao, and Yuan, Xiying
- Subjects
- *
EIGENVALUES , *GRAPH theory , *ORTHOGONAL functions , *REGULAR graphs - Abstract
An eigenvalue λ of a signed graph S of order n is a main eigenvalue if its eigenspace is not orthogonal to the all-ones vector j. Characterizing signed graphs with exactly k (1 ≤ k ≤ n) main eigenvalues is a problem in algebraic and graph theory that has been studied since 2020. Z. Stanić has noticed that a signed graph has exactly one main eigenvalue if and only if it is net-regular, and in this paper, we study signed graphs with exactly two distinct main eigenvalues by studying (0 , 1 , 2) -multi-graphs with exactly two distinct main eigenvalues. We partially characterize the case when the basic graphs of the (0 , 1 , 2) -multi-graphs are trees, and propose some problems for further research. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF