Families of graphs with chromatic zeros lying on circles

We define an infinite set of families of graphs, which we call [Formula Presented]-wheels and denote [Formula Presented], that generalize the wheel [Formula Presented] and biwheel [Formula Presented] graphs. The chromatic polynomial for [Formula Presented] is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at [Formula Presented] for [Formula Presented] even and [Formula Presented] for [Formula Presented] odd; and (ii) the complex zeros all lie, equally spaced, on the unit circle [Formula Presented] in the complex [Formula Presented] plane. In the [Formula Presented] limit, the zeros on this circle merge to form a boundary curve separating two regions where the limiting function [Formula Presented] is analytic, viz., the exterior and interior of the above circle. Connections with statistical mechanics are noted.