Adjacent vertex distinguishing total coloring of planar graphs

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  An adjacent vertex distinguishing total coloring of a graph G , or avd-total coloring in short, is a proper total coloring of G such that any pair of adjacent vertices see distinct sets of colors.The minimum number of colors needed for an avd-total coloring of G is denoted by xa (G).We will present some results on avd-total coloring of planar graphs.
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