Adjacent vertex distinguishing total coloring of planar graphs with large maximum degree

Abstract

An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors needed for an adjacent vertex distinguishing total coloring of G is denoted by χa′′( G ). In this paper, we prove that every planar graph G with Δ( G ) ≥ 11 has χa′′( G ) ≤ Δ( G ) + 3.