The Aα-spectral radius for path-factors in graphs

S Zhou, Y Zhang, Z Sun - Discrete Mathematics, 2024 - Elsevier
Abstract Let α∈[0, 1), and let G be a connected graph of order n with n≥ f (α), where f (α)=
14 for α∈[0, 1 2], f (α)= 17 for α∈(1 2, 2 3], f (α)= 20 for α∈(2 3, 3 4] and f (α)= 5 1− α+ 1 for …

[HTML][HTML] On the Aα-spectra of graphs

H Lin, J Xue, J Shu - Linear Algebra and its Applications, 2018 - Elsevier
Let G be a graph with adjacency matrix A (G) and let D (G) be the diagonal matrix of the
degrees of G. For any real α∈[0, 1], Nikiforov [8] defined the matrix A α (G) as A α (G)= α D …

The Aα-spectral radius of trees and unicyclic graphs with given degree sequence

D Li, Y Chen, J Meng - Applied Mathematics and Computation, 2019 - Elsevier
For any real α∈[0, 1], A α (G)= α D (G)+(1− α) A (G) is the A α-matrix of a graph G, where A
(G) is the adjacency matrix of G and D (G) is the diagonal matrix of the degrees of G. This …

[HTML][HTML] Bounds for the largest and the smallest Aα eigenvalues of a graph in terms of vertex degrees

S Wang, D Wong, F Tian - Linear Algebra and its Applications, 2020 - Elsevier
Let G be a graph with adjacency matrix A (G) and with D (G) the diagonal matrix of its vertex
degrees. Nikiforov defined the matrix A α (G), with α∈[0, 1], as A α (G)= α D (G)+(1− α) A (G) …

[HTML][HTML] On the second largest Aα-eigenvalues of graphs

Y Chen, D Li, J Meng - Linear Algebra and its Applications, 2019 - Elsevier
Let G be a graph with adjacency matrix A (G) and the degree diagonal matrix D (G). For any
real α∈[0, 1], Nikiforov (2017)[10] defined the matrix A α (G) as A α (G)= α D (G)+(1− α) A …

[HTML][HTML] The Aα spectral radius characterization of some digraphs

J Liu, X Wu, J Chen, B Liu - Linear algebra and its applications, 2019 - Elsevier
Let λ (D) be the A α spectral radius of digraph D, and let G nr be the set of digraphs with
order n and dichromatic number r. In this paper, we characterize the digraph which has the …

[HTML][HTML] On the least eigenvalue of Aα-matrix of graphs

S Liu, KC Das, S Sun, J Shu - Linear Algebra and its Applications, 2020 - Elsevier
Let G be a graph of order n with m edges and chromatic number χ. Let A (G) be the
adjacency matrix and D (G) be the diagonal matrix of vertex degrees of G. Nikiforov defined …

On the Dα-spectra of graphs

H Lin, J Xue, J Shu - Linear and Multilinear Algebra, 2021 - Taylor & Francis
Let G be a connected graph with distance matrix D (G), and let T r (G) be the diagonal matrix
of vertex transmissions of G. For any α∈[0, 1], the D α-matrix of G is defined as D α (G)= α T r …

[HTML][HTML] On the eigenvalues of Aα-matrix of graphs

S Liu, KC Das, J Shu - Discrete Mathematics, 2020 - Elsevier
Let G be a graph with adjacency matrix A (G) and let D (G) be the diagonal matrix of the
degrees of G. For every real α∈[0, 1], Nikiforov defined the matrix A α (G) as A α (G)= α D …

The Aα-spectral radius and perfect matchings of graphs

Y Zhao, X Huang, Z Wang - Linear Algebra and its Applications, 2021 - Elsevier
Abstract Let α∈[0, 1), and let G be a graph of even order n with n≥ f (α), where f (α)= 10 for
0≤ α≤ 1/2, f (α)= 14 for 1/2< α≤ 2/3 and f (α)= 5/(1− α) for 2/3< α< 1. In this paper, it is …