A Necessary and Sufficient Condition for a vertex-transitive Graph to be Star Extremal
Wensong Lin, Guohua Gu · Journal of Southeast University · 2004
A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. We first give a necessary and sufficient condition for a graph G to have circular chromatic number |V(G)|/α(G) (where |V(G)| is the vertex number of G and α(G) is its independence number). From this result, we get a necessary and sufficient condition for a vertex-transitive graph to be star extremal as well as a necessary and sufficient condition for a circulant graph to be star extremal. Using these conditions, we obtain several classes of star extremal graphs.