若干图的Smarandachely邻点可区别I-全染色

Smarandachely Adjacent Vertex-Distinguishing I-Total Coloring of Some Graphs

图G的Smarandachely邻点可区别I-全染色是一个满足相邻顶点色集合互不包含的点边关联关系不正常的全染色,把所用最少颜色数称为图G的Smarandachely邻点可区别I-全色数,应用构造函数的染色方法研究了简单图路、圈、星、扇、轮的Smarandachely邻点可区别I-全染色,并得到了这些图的Smarandachely邻点可区别I-全色数,从而验证了图的Smarandachely邻点可区别I-全染色猜想.

A vertex-edge abnormal total coloring of a graph is called a Smarandachely adjacent ver- tex-distinguishing I-total coloring if no two adjacent vertices whose color set exist the included re- lationship, and the minimum number of the required colors for this coloring is called the Sma- randachely adjacent vertex-distinguishing I-total chromatic number. In this paper, the Smaran- dachely adjacent vertex-distinguishing I-total colorings of path, cycle, star, fan and wheel are given by constructing colorable function, meanwhile, the Smarandachely adjacent vertex-distingguish- ing I-total chromatic number of path,cycle, star, fan and wheel are obtained, therefore, the Sma- randachely adjacent vertex-distinguishing I-total coloring conjecture is checked.