The Star Chromatic Numbers of Some Planar Graphs Derived from Wheels

The notion of the star chromatic number of a graph is a generalization of the chromatic number. In this paper, we calculate the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel by subdivisions, their star chromatic numbers being 2*2/(2n * 1), 2*3/(3n * 1), and 2*3(3n1), respectively. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 * 1/n, which is a generalization of one result of Gao et al.