The Adjacent Vertex Distinguishing Total Chromatic Number of Graphs
Zhiwen Wang, Enqiang Zhu · International Conference on Bioinformatics and Biomedical Engineering · 2010
Let G=(V,E) be a graph and f:(V ∪ E) → [k] be a proper total k-coloring of G. We say that f is an adjacent vertex distinguishing total coloring if for any two adjacent vertices, the set of colors appearing on the vertex and incident edges are different. We call the smallest k for which such a coloring of G exists the adjacent vertex distinguishing total chromatic number, and denote it by χat(G). In this paper, we show that χat(K19- E(C4)) = 20 and χat(K21-E(C4)) = 22.