Incidence coloring of Regular graphs and Complement graphs

Abstract

Using a relation between domination number and incidence chromatic number, we obtain necessary and sufficient conditions for $r$-regular graphs to be $(r+1)$-incidence colorable. Also, we determine the optimal Nordhaus-Gaddum inequality for the incidence chromatic number.

This paper have been withdrawn since the article to appear in Taiwanese Journal of Mathematics and it will offense the rules