图K_(2n+1)\E(2,m)的点可区别全染色

Vertex-distinguishing Total Coloring of K_(2n+1)\E(K_2,m)

图的点可区别全染色是1个任意2点色集合不同的正常全染色,其所用的最少颜色数被称为图的点可区别全色数,其中任意1点的色集合是指由该顶点的颜色以及与该顶点相关联的边的颜色构成的集合.结合平行线染色法给出了完全图K2n+1\E(K2,m)的染色方法,并研究了图K2n+1\E(2,m)(n≥2,m≥2)的点可区别全染色,得到了其点可区别全色数和相关猜想.

A proper total coloring of a simple graph G is called vertex distinguishing if for any two distinct vertices u and v in G,the set of colors assigned to the vertex u and edges incident to u differs from the set of colors assigned to the vertex v and edges incident to v.The minimal number of colors required for a vertex distinguishing total coloring of G is called the vertex distinguishing total coloring chromatic number.In this paper,the coloring method is given by combining with parallel lines method,and the vertex distinguishing total chromatic number of K2n＋1／E（K2,m） is discussed.Furthermore,a conjecture of complete graph K2n＋1 delete the edges of subgraph K2,m is given.