5 papers
A sharp bound for the least signless Laplacian eigenvalue of triangle-free graphs
Dongxiu Cai, Zhengbo Chen, Xiao-Dong Zhang
We prove that every finite simple triangle-free graph on vertices satisfies , where is the least eigenvalue of its signless Laplaci…
A finite threshold for the double-comet conjecture
Dongxiu Cai, Zhenbo Chen, Xiao-Dong Zhang
For a tree , let be the difference between its two largest adjacency eigenvalues. A balanced double comet is obtained by attaching equally many leaves to th…
The Equality Cases For the Laplacian Conjecture of Brouwer
Dongxiu Cai, Zhengbo Chen, Jia Yang +1
The Laplacian conjecture of Brouwer asserts that for any graph \(G\) of order n with \(m\) edges, the sum of the \(k\) largest Laplacian eigenvalues satisfies \(s_k(G) \le m + \bin…
The Equality Cases for the Grone-Merris-Bai Theorem
Dongxiu Cai, Zhengbo Chen, Jia Yang +1
The Grone--Merris inequality, conjectured by Grone and Merris~(1994) and first proved by Bai~(2011), states that for every graph of order and every , $\sum_{i=…
Sharp Bounds for Guiduli-Type Hereditary Spectral Problems
Dongxiu Cai, Jiasheng Zeng, Xiao-Dong Zhang
Guiduli asked in 1996 the following problem concerning the maximum spectral radius of a graph under hereditary density constraints. If an -vertex graph satisfies $e(H)\le c|…