Families of graphs with chromatic zeros lying on circles

We define an infinite set of families of graphs, which we call p-wheels and denote (Wh)(n)((p)) I that generalize the wheel (p=1) and biwheel (p=2) graphs. The chromatic polynomial for (Wh))(n)((p)) is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at q = 0,1,...,p + 1 for n - p even and q = 0,1....,p + 2 for n - p odd: and (ii) the complex zeros all lie, equally spaced, on the unit circle q-(p + 1)/=1 in the complex q plane. In the n-->(proportional to) limit, the zeros on this circle merge to form a boundary curve separating two regions where the limiting function W({(Wh)((p))},q) is analytic, viz., the exterior and interior of the above circle. Connections with statistical mechanics are noted.