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Isomorphism of graphs with bounded eigenvalue multiplicity

Authors:

László Babai,

D. Yu. Grigoryev,

David M. MountAuthors Info & Claims

STOC '82: Proceedings of the fourteenth annual ACM symposium on Theory of computing

Pages 310 - 324

https://doi.org/10.1145/800070.802206

Published: 05 May 1982 Publication History

Abstract

We investigate the connection between the spectrum of a graph, i.e. the eigenvalues of the adjacency matrix, and the complexity of testing isomorphism. In particular we describe two polynomial time algorithms which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity. If X and Y are graphs of eigenvalue multiplicity m, then the isomorphism of X and Y can be tested by an O(n^4m+c) deterministic and by an O(n^2m+c) Las Vegas algorithm, where n is the number of vertices of X and Y.

References

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Babai, L., "Monte Carlo algorithms in graph isomorphism testing," preprint, 1979.

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Babai, L., "Moderately exponential bound for isomorphism," Fundamentals of Computation Theory (Proc. Conf. FCT '81, Szeged; F. G-&-eacute;cseg, ed.) Lect. Notes in Comp. Sci. 117, Springer, 1981, 34-50.

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Cited By

Neuen D(2024)Isomorphism Testing for Graphs Excluding Small Topological SubgraphsACM Transactions on Algorithms10.1145/365198620:3(1-43)Online publication date: 21-Jun-2024
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cover image ACM Conferences

STOC '82: Proceedings of the fourteenth annual ACM symposium on Theory of computing

May 1982

408 pages

ISBN:0897910702

DOI:10.1145/800070

Copyright © 1982 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 05 May 1982

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https://dl.acm.org/doi/10.1145/3651986
Dym NGortler S(2024)Low-Dimensional Invariant Embeddings for Universal Geometric LearningFoundations of Computational Mathematics10.1007/s10208-024-09641-2Online publication date: 8-Feb-2024
https://doi.org/10.1007/s10208-024-09641-2
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https://doi.org/10.1007/s10115-023-01836-3
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https://doi.org/10.1007/978-3-031-24117-8_18
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