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A bound for the Aα-spectral radius of a connected graph after vertex deletion.
- Source :
- RAIRO: Operations Research (2804-7303); 2022, Vol. 56 Issue 5, p3635-3642, 8p
- Publication Year :
- 2022
-
Abstract
- G is a simple connected graph with adjacency matrix A(G) and degree diagonal matrix D(G). The signless Laplacian matrix of G is defined as Q(G) = D(G) + A(G). In 2017, Nikiforov [1] defined the matrix A<subscript>α</subscript>(G) = α D(G) + (1 − α)A(G) for α ∈ [0,1]. The A<subscript>α</subscript>-spectral radius of G is the maximum eigenvalue of A<subscript>α</subscript> (G). In 2019, Liu et al. [2] defined the matrix Θ<subscript>k</subscript>(G) as Θ<subscript>k</subscript> (G) = kD(G) + A(G), for k ∈ ℝ. In this paper, we present a new type of lower bound for the A<subscript>α</subscript>-spectral radius of a graph after vertex deletion. Furthermore, we deduce some corollaries on Θ<subscript>k</subscript> (G), A(G), Q(G) matrices. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 28047303
- Volume :
- 56
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- RAIRO: Operations Research (2804-7303)
- Publication Type :
- Academic Journal
- Accession number :
- 160041949
- Full Text :
- https://doi.org/10.1051/ro/2022176