Article ID Journal Published Year Pages File Type
4598783 Linear Algebra and its Applications 2016 11 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, , , , ,