Abstract:
Each cycle of a directed graph can be written as a linear combination of the circuits
of a cycle basis for that directed graph. We define two new classes of cycle bases and
show how each relates to the known classes of strictly fundamental cycle bases, zero-one
cycle bases and integral cycle bases. We provide examples showing the significance of the
Möbius band to constructing directed graphs, the bases of which are in some of these
classes and not in other classes.
