  Let $G$ be a connected graph. The resistance distance between any two
vertices of $G$ is equal to the effective resistance between them in the
corresponding electrical network constructed from $G$ by replacing each edge
with a unit resistor. The Kirchhoff index is defined as the sum of resistance
distances between all pairs of the vertices. Recently, Yang and Wang determined
the maximum Kirchhoff index of phenylene chains, and they proposed a conjecture
about the minimum Kirchhoff index. In this note, we characterized the minimum
phenylene chains with respect to the Kirchhoff index. This proves the
conjecture.
