Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598533 | Linear Algebra and its Applications | 2016 | 16 Pages |
Abstract
The Laplacian spread of a graph G with n vertices is defined to be sL(G)=μ1(G)−μn−1(G)sL(G)=μ1(G)−μn−1(G), where μ1(G)μ1(G), μn−1(G)μn−1(G) are the largest and the second smallest Laplacian eigenvalues of G , respectively. It is conjectured that sL(G)≤n−1sL(G)≤n−1. In this paper, we first establish a new sharp upper bound for sL(G)sL(G), and then use it to prove that the conjecture is true for t -quasi-regular graphs when t≤n−3+2/n. We also present some other partial solutions for this conjecture; in particular, we show that the conjecture holds for K3K3-free graphs. Finally, we give several sharp lower bounds for sL(G)sL(G) as well.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xiaodan Chen, Kinkar Ch. Das,