Adjacent Vertex Distinguishing Equitable E-Total Coloring Of Some Graphs

Let G be a simple graph. A total coloring f of is called adjacent vertex distinguishingequitable E-total coloring if no two adjacent vertices of receive the same color and noedge incident vertex assigned the same color, and for any two adjacent vertices u andv,there must beC u C v.whan’s more, the difference of the elements colored by any twocolors is not more than1And the minimal number of colors required for the adjacent vertexdistinguishing equitable E-total coloring of is called the adjacent vertex distinguishingequitable edge-total chromatic number.In this paper, the adjacent vertex distinguishing equitable E total coloring of someDouble graphs and Mycielski graphs、Join graphs、Cartesian product graphs are discussed byusing method of exhaustion and the combination analytic, and their adjacent vertexdistinguishing equitable-total chromatic number are obtained.There are five parts in this paper:In the first part,some fundamental concepts,terminologist and symbols are introduced.In the second part, the adjacent vertex distinguishing equitable E total coloring isgiven and some important results are introduced.In the third part, the adjacent vertex distinguishing equitable E total coloring of somedouble graphs and some graphs are mainly studied.In the forth part, the adjacent vertex distinguishing equitable E total coloring of somejoin graphs are mainly studied.In the last part, the adjacent vertex distinguishing equitable E total coloring of someCartesian product graphs are mainly studied.