The homology of the cycle matroid of a coned graph

The cone ˆG of a finite graph G is obtained by adding a new vertex p, called the cone point, and joining each vertex of G to p by a simple edge. We show that the rank of the reduced homology of the independent set complex of the cycle matroid of ˆG is the cardinality of the set of the edge-rooted forests in the base graph G. 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 G. c 2006 Elsevier Ltd. All rights reserved.

• Type: Journal
• Year: 2007
• Where: EJC
• Authors: Woong Kook
• Keywords: Edge-rooted Forests, EJC 2007, Independent Set Complex, Information Technology, Reduced Homology