Incidence coloring of the squares of some graphs

Abstract

The incidence chromatic number of G , denoted by χ i ( G ) , is the least number of colors such that G has an incidence coloring. In this paper, we determine the incidence chromatic number of the powers of paths, trees, which are min { n , 2 k + 1 } , and Δ ( T 2 ) + 1 , respectively. For the square of a Halin graph, we give an upper bound of its incidence chromatic number.