Abstract
The circular chromatic number χ c( G) and the fractional chromatic number χ 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−1, k, k+1,…, k+ m−2}, { k, k+1,…, k′}, and { k, k+1,…, k 1, k 2, k 2+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).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
