| A proper total coloring of a graph G is a coloring of its vertices and edges such that no adjacent vertices,edges,and no incident vertices and edges obtain the same color.A proper total-coloring of a graph G with colors 1,2,…,t is called an interval cyclic total t-coloring if all colors are used,and the colores of the edges incident to v and the vertex v insisted a cyclically interval.A graph G is interval cyclically colorable if it has an interval cyclic total t-coloring for some positive integer t,and denoted by St.The set of all interval cyclically total colorable graphs is denoted by S.For a graph S,the least and the greatest values of t for which it has an interval cyclic total t-coloring are denoted by wτc(G)and Wτc(G),respectively.For a graph G∈S,let(?)(G)= {t|G ∈St}.In this paper we investigated the interval cyclic total colorings of connected graph,Pn,Cn,Wn,Kn,Km,n,and Kl,m,n.In particu-lar,we proof these kinds of graph is interval cyclic total colorable.And we obtain all values of t of Pn,Cn,the least values of t of Wn、Kn、Km,m+1、Km,m+2、K1,m,n,and the bounds of the greatest values of t of Wn、Kn、Km,n、Kl,m.n. |
