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Complete signed graphs with largest maximum or smallest minimum eigenvalue.
- Source :
-
Discrete Mathematics . Apr2024, Vol. 347 Issue 4, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- In this paper, we deal with extremal eigenvalues of the adjacency matrices of complete signed graphs. The complete signed graphs with maximal index (i.e. the largest eigenvalue) with n vertices and m ≤ ⌊ n 2 / 4 ⌋ negative edges have been already determined. We address the remaining case by characterizing those with m > ⌊ n 2 / 4 ⌋ negative edges. We also identify the unique signed graph with maximal index among complete signed graphs whose negative edges induce a tree of diameter at least d for any given d. This extends a recent result by Li, Lin, and Meng [Discrete Math. 346 (2023), 113250] who established the same result for d = 2. Finally, we prove that the smallest minimum eigenvalue of complete signed graphs with n vertices whose negative edges induce a tree is − n 2 − 1 − 1 + O (1 n). [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
*REGULAR graphs
*COMPLETE graphs
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 347
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 175392400
- Full Text :
- https://doi.org/10.1016/j.disc.2023.113860