journal6 ›› 2009, Vol. 30 ›› Issue (4): 4-6.

• Mathematics • Previous Articles     Next Articles

Chromatic Number,Spectral Radius and Spanning Bipartite Subgraph


  1. (Faculty of Science,Huzhou Teachers’ College,Huzhou 313000,Zhejiang China)
  • Online:2009-07-25 Published:2012-04-22
  • About author:FANG Kun-fu(1963-),male,was born in Tongxiang,Zhejiang Province,associate professor;research area are graph theory and its applications.
  • Supported by:

    Natural Science Foundation of China (10671074)

Abstract: Let  G be a simple undirected graph with order n≥1.Denote by ρ(G) and μ(G) the spectral radius of the adjacency matrix and the Laplacian matrix of G,respectively.In this paper,by the way of spanning bipartite subgraphs,it is  showed that:let G be a simple graph with chromatic number k≥1.If k is even,ρ(G)≤(k-1)/kμ(G);if  k is odd,ρ(G)≤k/(k+1)μ(G).

Key words: spectral radius, Laplacian spectral radius, chromatic number, spanning bipartite subgraph

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