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In this paper, we have considered the finite, simple and undirected graphs. Let ( ( ), ( )) G V G E G  be a graph with the vertex set ( ) V G and the edge set ( ) E G respectively. In 1965, the concept of total coloring was introduced by Behzad [1] and in 1967, he [2] came out new ideology that, the total chromatic number of complete graph and complete bi-partite graph. A total coloring of G, is a function : f S C  , where ( ) ( ) S V G E G   and C is a set of colors to satisfies the given conditions.

Total Chromatic Number of Middle and Total Graph of Path and Sunlet Graph