Abstract
A general method is presented for testing graph isomorphism, which exploits those sufficient conditions that define linear orderings on the vertices of the graphs. The method yields simple and constructive, low-order polynomial graph isomorphism algorithms for classes of graphs which have a unique ordering, or a small (not necessarily bounded) number of different orderings. The general method is instantiated to several graph classes, including: interval graphs, outer-planar graphs, biconnected outerplanar graphs, and triconnected planar graphs. Although more efficient algorithms are known for isomorphism on some of these classes of graphs, the method can be applied to any class of graphs having a polynomial number of different orderings and an efficient algorithm for enumerating all these orderings.
Partially supported by the Spanish CICYT project TIC98-0949-C02-01 HEMOSS.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms. J. Comp. Syst. Sci., 13(3):335–379, 1976.
D. G. Corneil and D. G. Kirkpatrick. A theoretical analysis of various heuristics for the graph isomorphism problem. SIAM J. Comput., 9(2):281–297, 1980.
G. Gati. Further annotated bibliography on the isomorphism disease. J. Graph Theory, 3(1):95–109, 1979.
J. E. Hopcroft and R. E. Tarjan. An O(n logn) algorithm for isomorphism of triconnected planar graphs. J. Comp. Syst. Sci., 7(3):323–331, 1973.
X. Y. Jiang and H. Bunke. Optimal quadratic-time isomorphism of ordered graphs. Pattern Recogn., 32(7):1273–1283, 1999.
J. Köbler, U. Schöning, and J. Turán. The Graph Isomorphism Problem: its Structural Complexity. Progress in Theoretical Computer Science. Birkhäuser, 1993.
D. L. Kreher and D. R. Stinson. Combinatorial Algorithms: Generation, Enumeration, and Search. CRC Press, 1999.
S. L. Mitchell. Linear algorithms to recognize outerplanar and maximal outerplanar graphs. Inform. Process. Lett., 9(5):229–232, 1979.
R. C. Read and D. G. Corneil. The graph isomorphism disease. J. Graph Theory, 1(4):339–363, 1977.
U. Schöning. Graph isomorphism is in the low hierarchy. J. Comp. Syst. Sci., 37(3):312–323, 1988.
L. Weinberg. A simple and efficient algorithm for determining isomorphism of planar triply connected graphs. IEEE Trans. Circuit Theory, 13(2):142–148, 1966.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Valiente, G. (2001). A General Method for Graph Isomorphism. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_49
Download citation
DOI: https://doi.org/10.1007/3-540-44669-9_49
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42487-1
Online ISBN: 978-3-540-44669-9
eBook Packages: Springer Book Archive