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On Aα-spectrum of joined union of graphs and its applications to power graphs of finite groups.
- Source :
- Journal of Algebra & Its Applications; Dec2023, Vol. 22 Issue 12, p1-23, 23p
- Publication Year :
- 2023
-
Abstract
- For a simple graph G , the generalized adjacency matrix A α (G) is defined as A α (G) = α D (G) + (1 − α) A (G) , α ∈ [ 0 , 1 ] , where A (G) is the adjacency matrix and D (G) is the diagonal matrix of vertex degrees of G. This matrix generalizes the spectral theories of the adjacency matrix and the signless Laplacian matrix of G. In this paper, we find the A α -spectrum of the joined union of graphs in terms of the spectrum of the adjacency matrices of its components and the zeros of the characteristic polynomials of an auxiliary matrix determined by the joined union. We determine the A α -spectrum of join of two regular graphs, the join of a regular graph with the union of two regular graphs of distinct degrees. As applications, we investigate the A α -spectrum of certain power graphs of finite groups. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 22
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 173419511
- Full Text :
- https://doi.org/10.1142/S0219498823502572