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Some α-spectral extremal results for some digraphs.
- Source :
- Linear & Multilinear Algebra; 12/31/2022, Vol. 70 Issue 22, p7493-7514, 21p
- Publication Year :
- 2022
-
Abstract
- In this paper, we characterize the extremal digraphs with the maximal or minimal α-spectral radius among some digraph classes such as rose digraphs, generalized theta digraphs and tri-ring digraphs with given size m. These digraph classes are denoted by R<subscript>m</subscript><superscript>k</superscript>, ...(m) and ...(m) respectively. The main results about spectral extremal digraph by Guo and Liu [Some results on the spectral radius of generalized ∞ and θ-digraphs. Linear Algebra Appl. 2012;437(9):2200-2208] and Li et al. [The signless Laplacian spectral radius of some strongly connected digraphs. Indian J Pure Appl Math. 2018;49(1):113-127] are generalized to α-spectral graph theory. As a by-product of our main results, an open problem in Li et al. [The signless Laplacian spectral radius of some strongly connected digraphs. Indian J Pure Appl Math. 2018;49(1):113-127] is answered. Furthermore, we determine the digraphs with the first three minimal α-spectral radius among all strongly connected digraphs. Meanwhile, we determine the unique digraph with the fourth minimal α-spectral radius among all strongly connected digraphs for 0 ≤ α ≤ 1/2. [ABSTRACT FROM AUTHOR]
- Subjects :
- GRAPH theory
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 70
- Issue :
- 22
- Database :
- Complementary Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 171945516
- Full Text :
- https://doi.org/10.1080/03081087.2021.1996523