The smallest integer $k$ needed for the assignment of colors to the elements
so that the coloring is proper (vertices and edges) is called the total
chromatic number of a graph. Vizing and Behzed conjectured that the total
coloring can be done using at most $\Delta(G)+2$ colors, where $\Delta(G)$ is
the maximum degree of $G$.
  It is not settled even for planar graphs. In this paper we give a survey on
total coloring of graphs.Comment: 23 pages, 3 figures 1 tabl

Jayabalan, Geetha