龙虾树的多级距离标号

The Multi-level Distance Labeling for Lobster Tree

连通图G的多级距离标号是指顶点集V(G)到{0,1,2,…}的一个映射f,它使得对于任意的u,v∈V(G)满足:|f(u)-f(v)|≥diam(G)+1-d(u,v),其中diam(G)是图G的直径,d(u,v)是两点u,v之间的距离.函数f的跨度是指(?){f(u)-f(v)}.图G的多级距离数是指它的所有多级距离标号的最小跨度.本文研究了一类关于权中心点对称的龙虾树,并得出了它的多级距离数的一个下界,进而得出了它在某些特殊情况下的多级距离数的确切值.

The multi-level distance labeling for a connected graph G is a flmction f ：V（G） → {0,1,2,...}, so that the following is satisfied for u,v C V（G）： ｜f（u） - f（v）｜≥ diam （G） ＋ 1 - d（u, v）, where diam （G） is the diameter of G, d（u, v） is the distance between u,v. The span of f is defined as max {f（u） - f（v）}. The multi-level distance number of u,veV（G） G is the minimum span of a multi-levei distance labeling for G. A class of symmetric lobster tree about weight center is investigated, and its a lower bound of the multi-level distance number is obtained, and then the exact number in some special cases of the multi-level distance number is obtained.