1. The Laplacian spread of quasi-tree graphs
- Author
-
Jixiang Meng and Ying Xu
- Subjects
Discrete mathematics ,Numerical Analysis ,Algebraic connectivity ,Algebra and Number Theory ,Resistance distance ,Unicyclic graphs ,Graph theory ,Mathematics::Spectral Theory ,Quasi-tree graph ,Combinatorics ,Laplacian spread ,Discrete Mathematics and Combinatorics ,Geometry and Topology ,Laplacian matrix ,Laplace operator ,Connectivity ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. Bao, Tan and Fan [Y.H. Bao, Y.Y. Tan,Y.Z. Fan, The Laplacian spread of unicyclic graphs, Appl. Math. Lett. 22 (2009) 1011–1015.] characterize the unique unicyclic graph with maximum Laplacian spread among all connected unicyclic graphs of fixed order. In this paper, we characterize the unique quasi-tree graph with maximum Laplacian spread among all quasi-tree graphs in the set Q ( n , d ) with 1 ⩽ d ⩽ n - 4 2 .
- Published
- 2011