关于连通图的IC-着色

On IC-colorings of Connected Graphs

文[2]中引入了图的IC-着色和IC-指数概念,本文考虑了两个图的和图IC-指数,证明了:对任意连通图G和H,均有M(G+H)(M(G)+1)(M(H)+1)-1,并给出了星的任意细分图IC-指数的一个下界,推广了文[2]中的两个结果.

The concept of IC-colorings and IC-indices of graphs was introduced in [2]. In this paper we consider the ICindices in the sum graph of two graphs, show that M（G＋H）≥（M（G）＋1）（M（H）＋1）-1 holds for any two connected graphs G and H, and give a lower bound of the IC-indices for any subdivision of stars, which generalize some resuits in [2].