A Mechanical Analysis of the Cyclic Structure of Undirected Linear Graphs
Journal of the ACM (JACM)
GIT—a heuristic program for testing pairs of directed line graphs for isomorphism
Communications of the ACM
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A Cycle Generation Algorithm for Finite Undirected Linear Graphs
Journal of the ACM (JACM)
An Efficient Algorithm for Graph Isomorphism
Journal of the ACM (JACM)
Algorithms for Generating Fundamental Cycles in a Graph
ACM Transactions on Mathematical Software (TOMS)
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Communications of the ACM
An efficient search algorithm to find the elementary circuits of a graph
Communications of the ACM
An algorithm for finding a fundamental set of cycles of a graph
Communications of the ACM
Circuit enumeration in an undirected graph
ACM-SE 16 Proceedings of the 16th annual Southeast regional conference
A planarity algorithm based on the Kuratowski theorem
AFIPS '70 (Spring) Proceedings of the May 5-7, 1970, spring joint computer conference
Benchmarks for strictly fundamental cycle bases
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
| Hi-index | 48.26 |
Given the adjacency matrix of the graph, the algorithm presented in this paper finds a spanning tree and then constructs the set of fundamental cycles. Our algorithm is slower than an algorithm presented by Welch by a ratio of N/3 (N is the number of nodes) but requires less storage. For graphs with a large number of nodes and edges, when storage is limited our algorithm is superior to Welch's; however, when the graphs are small, or machine storage is very large, Welch's algorithm is superior. Timing estimates and storage requirements for both methods are presented.