若干图的强染色(英文)

ON THE STRONG COLORING OF SOME GRAPHS

图 G(V,E)的一正常 k-染色 σ称为 G(V,E)的 - k-强染色当且仅当对任何两个不同顶点 u和 v,只要d(u,v)≤ 2 ,则 u、v染不同颜色 (这里 d(u,v)表示 u,v之间的距离 ) ,并称 xs(G) =min{ k|存在 G的 - k-强染色 }为 G的强色数 ,本文得到 θ-图 ,Cm,n图 ,Halin图的强色数 xs(G)

A proper k coloring σ of graph G(V,E) is said to be a k strong coloring of G(V,E ) iff for any two vertices u and v with d(u,v )2 have distinct colors,where d(u,v ) denotes the distance between the vertices u and v ,and x s(G)= min{ k|k -strong coloring of G }is called the strong chromatic number of G .In this paper,we obtained some results about x s(G) of θ-graph. C m,n ,graph, Halin graph.