路图的Smarandachely全染色算法*

设f是简单图G的一个正常的k-全染色，若G中任意两点的点及其关联边的颜色构成的集合互不包含，则称f为G的k-Smarandachely全染色，这样的k中最小者称为G的Smarandachely全色数。针对路图的Smarandachely全染色问题，提出了一种新算法。算法采用三元组编码方式将问题进行转化，按照给定规则生成三元组队列，并对该队列内部排序进行变换调整。同时，给出两个判断函数，根据函数的值判断是否得到问题的解。实验结果表明，该算法可以有效地解决路图的Smarandachely全染色问题。

Algorithm for Smarandachely total coloring of paths

Let f be a proper k- total coloring of a simple graph G .If there is no inclusion relation for any two sets made up of colors of vertex and its associated edges, f is called a k-Smarandachely total coloring of G and the minimum value of k is called Smarandachely coloring chromatic number of G. To solve the problem of the Smarandachely total coloring of paths, a new algorithm was proposed. The problem was converted by means of the triple coding method. According to some rules, the triple queue was produced and the internal sequence of the queue was changed and adjusted. Moreover, two judging functions were presented and whether the result was correct was judged by the value of the functions. The experimental results show that this algorithm can effectively solve the Smarandachely total coloring of paths.