摘要
设f:V(G)∪E(G)→{1,2,…,k}是图G的一个正常k-全染色。令φ(x)=f(x)+eЭx/∑f(e)+∑y∈N(x)/∑f(y),其中N(x)={y∈V(G)|xy∈E(G)}。对任意的边uv∈E(C),若有Φ(u)≠Φ(v)成立,则称f是图G的一个邻点全和可区别k-全染色。图G的邻点全和可区别全染色中最小的颜色数k叫做G的邻点全和可区别全色数,记为f tndi∑(G)。本文确定了路、圈、星、轮、完全二部图、完全图以及树的邻点全和可区别全色数,同时猜想:简单图G(≠K2)的邻点全和可区别全色数不超过△(G)+2。
Let f:V(G)∪E(G)→{1,2,…,k}be a proper k-total coloring of G.Set φ(x)=f(x)+eЭx/∑f(e)+∑y∈N(x)/∑f(y) where N(x)={y∈V(G)|xy∈E(G)}.IfΦ(u)≠Φ(v)for any edge uv∈E(G),then.f is called a k-neighbor full sum distinguishing total coloring of G.The smallest value k for which G has such a coloring is called the neighbor full sum distinguishing total chromatic number of G and denoted by ftndi∑(G).In this paper,we obtain this parameter for paths,cycles,stars,wheels,complete bipartite graphs,complete graphs and trees.Meanwhile,we conjecture that the neighbor full sum distinguishing total chromatic number of C(≠K2)is not more than△(G)+2.
作者
崔福祥
杨超
叶宏波
姚兵
CUI Fuxiang;YANG Chao;YE Hongbo;YAO Bing(School of Mathematics,Physicsand Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;Center of Intelligent Computing and Applied Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)
出处
《运筹学学报》
CSCD
北大核心
2023年第1期149-158,共10页
Operations Research Transactions
基金
国家自然科学基金(Nos.61163054,61363060,61662066)。
关键词
正常全染色
可区别染色
邻点全和可区别全染色
邻点全和可区别全色数
proper total coloring
distinguishing coloring
neighbor full sum distinguishing total coloring
neighbor full sum distinguishing total chromatic number