10.3969/j.issn.1005-3085.2012.05.020
The Spectrum of a Graph Obtained from Copies of a Generalized Bethe Tree and a Complete Graph?
A generalized Bethe tree is a rooted tree for which the vertices in each level having equal degree. Let Bk be a generalized Bethe tree of k level, and let Kr be a complete graph on r vertices. Then a graph Bk?Kr is obtained from r copies of Bk and Kr by appending r roots to the vertices of Kr, respectively. In this paper, a simple way is introduced to characterize the eigenvalues of the adjacency matrix A(Bk?Kr) and the Laplacian matrix L(Bk?Kr) of Bk?Kr by means of symmetric tridiagonal matrices of order k. In addition, the structure property of the Perron vectors of A(Bk?Kr) is given.
Bethe tree、Laplacian matrix、adjacency matrix、algebraic connectivity、Perron vector
O157.5(代数、数论、组合理论)
2012-11-06(万方平台首次上网日期,不代表论文的发表时间)
共10页
763-772