A Mechanical Analysis of the Cyclic Structure of Undirected Linear Graphs
Journal of the ACM (JACM)
A Cycle Generation Algorithm for Finite Undirected Linear Graphs
Journal of the ACM (JACM)
An algorithm for finding a fundamental set of cycles of a graph
Communications of the ACM
Algorithms for finding a fundamental set of cycles for an undirected linear graph
Communications of the ACM
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In his paper J. T. Welch [7] presents an algorithm for determining the circuits of a graph in a mechanical manner. Unfortunately, when an implementation of this procedure was attempted by N. E. Gibbs a very large class of counter examples was discovered. Gibbs rectified this situation in his algorithm [1]. However, a close study of Gibbs' algorithm shows that it is essentially an enumerative case considering all possible combinations. Hsu and Honkanen [3] developed a set of algorithms which used Welch's Concept where it applied and then examined the remaining circuits essentially in a manner like Gibbs' algorithm but did not require examining all possible combinations. R. Tarjan [6] pointed out several flaws in these algorithms which are corrected in this paper.