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Adjacent Vertex Distinguishing Total Coloring on the Middle Graphs

Let G be a simple connected graph..A k-proper total coloring of G is called adjacent distinguishing if for arbitrary two adjacent vertices u and v,C(u)≠ C(v),where C(u) is the set of the colors of u and edges which is adjacent tou.The minimumk such thatG has a k-adjacent-vertex-distinguishing total coloring is called the adjacent vertex distinguishing total chromatic number.The adjacent vertex distinguishing total chromatic number is obtained for the middle graphs of path,cycle,star and fan graph.