Probe of schemes for vertex strongly distinguishing total coloring of complete bipartite graph K 5,7

DOI：10.7511/dllgxb201603014

 作者 单位 王蓓蓓,祁丽娟,刘信生,陈祥恩

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K 5,7 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<2m-2时，那么χ vst (K m,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 of complete bipartite graph K 5,7 is discussed using the method of combinatorial analysis. Then, based on the discussion, two schemes about the vertex strongly distinguishing total coloring of complete bipartite graph K 5,7 are put forward. The results not only help to determine the vertex strongly distinguishing total chromatic number of complete bipartite graph K 5,7 which is equal to nine, but also negate the conjecture proposed by Hu Zhi-tao: ″If m ≥4 and n<2m-2 , then χ vst ( K m,n )=n+3 ″ when m =5. Furthermore, the scope which makes this conjecture established is determined.