广义Petersen图在四种可区分条件下的全染色（英文）

Generalized Petersen graphs admit proper total colorings with four distinguishing constraints

关于图的可区别染色的研究起源于移动通信的频率分配问题.本文定义了简单图G的一个4-邻点可区别全染色.对一个图G进行4-邻点可区别全染色所需的最少颜色数称为图G的4-邻点可区别全色数,记为x〃_(4as)(G).对于广义Petersen图P(n,k),6≤x〃_(4as)(P(n,k))≤7得到证明.

The study of distinguishing coloring in graphs is derived from the frequency assignment problem in mobile communications.This paper introduced the concept of 4-adjacent vertex distinguishing total coloring （4-avdtc） of a simple graph G.The minimum number of k colors required for G such that it satisfies a 4-avdtc is denoted as x＂4as（G）.For generalized Petersen graphs P（n,k）,it was proved that 6 ≤ x＂4as（P（n,k）） ≤ 7.