Name
Abstract | ||
|---|---|---|
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 Aα(G) as Aα(G)=αD(G)+(1−α)A(G). In this paper, we study the kth largest eigenvalue of Aα-matrix of graphs, where 1≤k≤n. We present several upper and lower bounds on the kth largest eigenvalue of Aα-matrix and characterize the extremal graphs corresponding to some of these obtained bounds. As applications, some bounds we obtained can generalize some known results on adjacency matrix and signless Laplacian matrix of graphs. Finally, we solve a problem proposed by Nikiforov (2017). |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.disc.2020.111917 | Discrete Mathematics |
Keywords | DocType | Volume |
Graph,The kth largest eigenvalue of Aα(G),Aα-spectral radius,Degree | Journal | 343 |
Issue | ISSN | Citations |
8 | 0012-365X | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shuting Liu | 1 | 0 | 0.34 |
| Kinkar Chandra Das | 2 | 0 | 0.34 |
| Jinlong Shu | 3 | 99 | 24.28 |