K3,5,p的点可区别的一般全染色

Vertex-Distinguishing General Total Coloring of K 3,5,p

首先,利用色集合事先分配法,反证探讨完全三部图K3,5,p(p≥5)的点可区别一般全色数,给出当p较小时的特殊性证明以及当p逐渐增大时的规律性证明;其次,利用构造染色法对完全三部图K3,5,p进行染色,给出染色方案.染色的成功验证了反证法所证明色数的正确性,从而解决了完全三部图K3,5,p的点可区别一般全染色问题.

Firstly,we discussed vertex-distinguishing general total chromatic number of complete tripartite graphs K 3,5,p(p≥5)by using the method of distributing the color sets in advance and contradiction,and gave special proofs when p was small and regular proofs when p increased gradually.Secondly,we used the methods of constructing the colorings to dye the complete tripartite graphs K 3,5,p,and gave a coloring scheme.The success of the coloring verified the correctness of the color number proved by the contradiction method,thus we solved the problem of vertex-distinguishing general total coloring of complete tripartite graphs K 3,5,p.