An all cycle algorithm for undirected graphs

TLDR: In this paper, an algorithm for finding the fundamental cycle set from a spanning tree and a branch and bound option which will find the longest cycle in a graph is presented, which is based on a more efficient branching procedure than was used previously.

Abstract: An algorithm is presented which generates, without duplication, all the simple cycles of an undirected graph. The algorithm employs the concept of a fundamental cycle set and is based on a more efficient branching procedure than was used previously.1,2 As a consequence both execution time and storage requirements are greatly reduced. Also included is an improved method for finding the fundamental cycle set from a spanning tree, and a branch and bound option which will find the longest cycle in a graph.