Deteeting all cycles in connected undirected planar networks

In this paper, we propose an algorithm to achieve two goals; one, which we call enumerating, is determining how many simple cycles there are in a planar network. The other, which we call detecting, is the construction of every cycle in the network exactly once besides calculating some properties. The proposed method is based on breadth-first search and is applicable in dual of the planar network. The algorithms run in o(n2).

Keywords:

Planar networks , dual network , cycles