图Pm×P3 (n=11+8k)的点可区别全染色与算法

journal6 ›› 2011, Vol. 32 ›› Issue (6): 5-10.

图Pm×P3 (n=11+8k)的点可区别全染色与算法

(1.兰州城市学院信息工程学院,甘肃兰州 730070；2.兰州交通大学应用数学研究所,甘肃兰州 730070)

出版日期:2011-11-25 发布日期:2012-03-22
作者简介:包世堂(1970-),男,甘肃定西人,兰州城市学院信息工程学院副教授,主要从事信息与计算科学研究.
基金资助:
国家自然科学基金资助项目(11061017)；甘肃省教育厅科研项目(1111B-04)

Vertex-Distinguishing Total Coloring of Graph Pm×P3(n=11+8k) and the Algorithm

(1.School of Information Science and Engineering,Lanzhou City University,Lanzhou 730070,China;2.Institute of Applied Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China)

Online:2011-11-25 Published:2012-03-22

摘要/Abstract

摘要：集合{1,2,…,n}中取4个数字的所有组合，经三角排序后任意相邻2个组合都有3个相同数字.利用此结果和组合性质n+8k3-n3≡ 0 (mod 4)构造算法，并证明当n=11+8k(k=0,1,…)和n-14/2+2 <m≤n4/2+2时积图Pm×P3的点可区别全色数为n.

关键词： 积图, 点可区别全染色, 点可区别全色数, 三角排序

Abstract: Let A be a set consisted of all combinations which are made up of four numbers selected from the set {1,2,…,n} discretionarily.By the triangle compositor,the author obtain that for any two adjacent elements C and D in set A,they contain the same three elements.In this paper,using the above idea and n+8k3-n3≡0 (mod 4),it is proved that when n=11+8k(k=0,1,…) and n-14/2+2 <m≤n4/2+2,vertex distinguishing total chromatic number of product Pm×P3 is n.

Key words: product graph, vertex distinguishing toal coloring, vertex distinguishing total chromatic number, triangle sequence

包世堂, 韩晓红, 李沐春, 文飞. 图Pm×P3 (n=11+8k)的点可区别全染色与算法[J]. journal6, 2011, 32(6): 5-10.

BAO Shi-Tang, HAN Xiao-Hong, LI Mu-Chun, WEN Fei. Vertex-Distinguishing Total Coloring of Graph Pm×P3(n=11+8k) and the Algorithm[J]. journal6, 2011, 32(6): 5-10.

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