  We define an infinite set of families of graphs, which we call $p$-wheels and
denote $(Wh)^{(p)}_n$, that generalize the wheel ($p=1$) and biwheel ($p=2$)
graphs. The chromatic polynomial for $(Wh)^{(p)}_n$ 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 $n \to \infty$ 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.
