ABSTRACT
There are numerous interesting and useful graph invariants associated with the cycle space of a graph. Of particular interest are certain “efficient” bases called minimum cycle bases. These ideas have a long history in applied discrete mathematics, going back at least as far as G. Kirchhoff’s (1847) treatise on electrical networks. More recently, Berger, Flamm, Gleiss, Leydold, and Stadler (2004) describe an application of minimum cycle bases to the problem of characterizing molecular graphs. See Kaveh (1995) for applications to structural flexibility analysis. Kaveh and Mirzaie (2008) apply minimum cycle bases of Cartesian and strong products to the force method of frame analysis.
