完全二部图K_(5,7)点强可区别全染色方案探讨  

Probe of schemes for vertex strongly distinguishing total coloring of complete bipartite graph K_(5,7)

作　　者：王蓓蓓[1] 祁丽娟[2] 刘信生[1] 陈祥恩[1] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070 [2]兰州工业学院基础学科部,甘肃兰州730050

出　　处：《大连理工大学学报》2016年第3期309-312,共4页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(61163037;61163054;61363060)

摘　　要：利用组合分析的方法先讨论了完全二部图K_(5,7)的点强可区别全染色,在此基础之上给出了两种具体的关于完全二部图K_(5,7)的点强可区别全染色方案.此结果的给出不仅确定了完全二部图K5,7的点强可区别全色数为9,而且对于胡志涛所提出的关于完全二部图的点强可区别全染色的猜想:"如果m≥4且n<2 m-2时,那么χvst(Km,n)=n+3"中当m=5时作出了否定,从而进一步确定了此猜想成立的范围.Firstly, the vertex strongly distinguishing total coloring discussed using the method of combinatorial analysis. Then, base about the vertex strongly distingu forward. The results not only help number of complete proposed by Hu Zhb ishing total coloring of comp of complete bipartite graph K5,7 is on the discussion, two schemes te bipartite graph K5,7 are put to determine the vertex strongly distinguishing total chromatic bipartite graph Ks,7 which tao： ＂If m≥4 and n〈2m-2, e scope which makes this conjecture established is equal to nine, but also negate the conjecture then xvst,（Km,n） =n＋3＂ when m=5. Furthermore, is determined.

关 键 词：正常全染色 完全二部图 点强可区别全染色 点强可区别全色数 

分 类 号：O157.5[理学—数学]