  In 6, Radchenko and Villegas characterized the chordal graphs by their
inverse of the independence polynomials being Horn hypergeometric series. In
this paper, we reprove their result using some elementary combinatorial methods
and also generalize it to PEO graphs that could have a countable number of
vertices. Our proof is different from the proof of 6, and it is based on the
connection between the inverse of the multi-variate independence polynomials
and the multi-colored chromatic polynomials of graphs, established in 1.
