The Adjacent Vertex Distinguishing Total Coloring Of Four Types Of Graphs

Let G be a connected graph of order greater than or equal to 2 and k be a positive integer. If f is a mapping from V(G)∪E(G) to{1,2,…,k}, which satisfies① for ; ② for ;③ for , where C(u) = {f(u)}∪{f(uv)|uv∈E(G)}, then we call f a k -adjacent distinguishing total coloring of G , abbreviated ask-AVDTC , and x_at(G) = min{k|k-AVDTC of G} the adjacent vertexdistinguishing total chromatic number.In this dissertation we shall study the adjacent vertex distinguishing totalcoloring of four types of graphs.① We shall discuss the adjacent vertex distinguishing total coloring of the cartesian product graphs and get the results as follows:a. If and② We shall determine the adjacent vertex distinguishing total chromatic number of Mycielski graphs of tree.Let T be a tree of order n , △(T) = △. If 2 A ≥ n and E(T[V_△ ]) = Φ, then③ We shall determine the adjacent vertex distinguishing total chromatic number...