The chromatic number of 5-valent circulants

A circulant C(n;S) with connection set S={a"1,a"2,...,a"m} is the graph with vertex set Z"n, the cyclic group of order n, and edge set E={{i,j}:|i-j|@?S}. The chromatic number of connected circulants of degree at most four has been previously determined completely by Heuberger [C. Heuberger, On planarity and colorability of circulant graphs, Discrete Math. 268 (2003) 153-169]. In this paper, we determine completely the chromatic number of connected circulants C(n;a,b,n/2) of degree 5. The methods used are essentially extensions of Heuberger's method but the formulae developed are much more complex.