Abstract
Let G be a planar graph. The vertex face total chromatic number χ13(G) of G is the least number of colors assigned to V(G)∪F(G) such that no adjacent or incident elements receive the same color. The main results of this paper are as follows: (1) We give the vertex face total chromatic number for all outerplanar graphs and modulus 3-regular maximal planar graphs. (2) We prove that if G is a maximal planar graph or a lower degree planar graph, i.e., ∠(G) ≤ 3, then χ13(G) ≤ 6. © 1996 John Wiley & Sons, Inc.
