Some star extremal circulant graphs Original Research Article

The circular chromatic number χc(G) and the fractional chromatic number χf(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−1,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).