The Smarandachely Adjacent-Vertex Total Coloring of Generalized 3-Regular Ring Graph

The Smarandachely adjacent-vertex total chromatic number of graph G is the smallest positive integer k for which G has a proper total k-coloring such that for any pair of adjacent vertices u,v, the set of colors appearing at vertex u and its incident edges is not a subset of the set of colors appearing at vertex v and its incident edges. In this paper, a kind of Generalized 3-regular Ring Graph is defined, and the Smarandachely adjacent-vertex total chromatic numbers is discussed by using construct coloring function. Furthermore, the conjecture of Smarandachely adjacent-vertex total coloring of 3-regular graph is checked.