摘要
给定一个包含0的有限正整数集T,一个简单图G的一个T-染色是定义在G的顶点集V(G)上的一个非负函数f,满足对任意的uv∈E(G)有|f(u)-f(v)| T.一个T-染色f的边柞(edgespan)定义为最大的|f(x)-f(y)|,xy∈E(G),一个图G的边柞(edgespan)是G的所有T-染色中最小的边柞(edgespan).这篇文章研究了当T={0,1,2,…,k-1}时,Gdn图的T-边柞(edgespan),找到了当n≡1(modd)时Gdn图的T-边柞(edgespan)的确切值,和其他情况下的上下界.
Suppose G is a graph and T is a set of non-negative integers that contains -. A T-coloring of G is an assignment of a non-negative integer f(x) to each vertex x of G such that |f(x)-f(y)|T whenever xy ∈E(G). The edge span of a T-coloring f is the minimum value of the edge span of a T-coloring of G. This paper studies the T-edge span of the G^d_n for T={-,1,2,...,k-1}. In particular, we find the exact value of the T-edge span of G^d_n for n≡-,1 (mod d+1), and lower and upper bounds for other cases.
出处
《纯粹数学与应用数学》
CSCD
2003年第4期361-364,共4页
Pure and Applied Mathematics
