Abstract:

A proper total coloring of G is an adjacent vertex distinguishing total coloring if for any two adjacent vertices, the sets of colors appearing on the vertex and incident edges are different. The smallest number of color of which such a coloring of G exists is called the adjacent vertex distinguishing total chromatic number, and is denoted by χ_at(G). It is proved that χ_at (G)≤Δ(G)+2 for any planar bipartite graph G with maximum degree Δ(G) at least 11 and grith at least 4.

Key words:  graphs; planar bipartite graphs; adjacent-vertex-distinguishing total coloring; adjacent-vertex-distinguishing total chromatic number