Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598783 | Linear Algebra and its Applications | 2016 | 11 Pages |
Abstract
A connected graph G with maximum degree Δ and edge chromatic number χ′(G)=Δ+1χ′(G)=Δ+1 is called Δ-critical if χ′(G−e)=Δχ′(G−e)=Δ for every edge e of G . In this paper, we consider two weaker versions of Vizing's conjecture, which concern the spectral radius ρ(G)ρ(G) and the signless Laplacian spectral radius μ(G)μ(G) of G . We obtain some lower bounds for ρ(G)ρ(G) and μ(G)μ(G), and present some cases where the conjectures are true. Finally, several open problems are also proposed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Lihua Feng, Jianxiang Cao, Weijun Liu, Shifeng Ding, Henry Liu,