The homology of the cycle matroid of a coned graph

The cone Gˆ of a finite graph GG is obtained by adding a new vertex pp, called the cone point, and joining each vertex of GG to pp by a simple edge. We show that the rank of the reduced homology of the independent set complex of the cycle matroid of Gˆ is the cardinality of the set of the edge-rooted forests in the base graph GG. We also show that there is a basis for this homology group such that the action of the automorphism group Aut(G) on this homology is isomorphic (up to sign) to that on the set of the edge-rooted forests in GG.