Some star extremal circulant graphs

The circular chromatic number chi(c)(G) and the fractional chromatic number chi(f)(G) are two generalizations of the ordinary chromatic number of a graph G. A graph is called star extremal if its circular chromatic number equals its fractional chromatic number. Gao and Zhu (Discrete Math. 152 (1996) 147-156), Lih et al. (SIAM J. Discrete Math. 12 (1999) 491-499) gave many classes of circulant graphs which are star extremal. In this paper, we study the star extremality of circulant graphs whose generating sets are of the form {1,2,...,m - l,k,k+ 1,...,k+m -2}, {k,k + 1,....,k'} and {k,k + 1,....,k1,k2,k2 + 1,....,[p/2]} , where p is the vertex number of the graph. As a corollary, we give an improvement of a result of Gao and Zhu (Discrete Math. 152 (1996) 147-156). (C) 2003 Elsevier B.V. All rights reserved.