Proceedings ArticleDOI
Isomorphism of graphs with bounded eigenvalue multiplicity
László Babai,D. Yu. Grigoryev,David M. Mount +2 more
- pp 310-324
TLDR
Two polynomial time algorithms are described which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity, if X and Y are graphs of eigenvalue multiplicity m.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(n4m+c) deterministic and by an O(n2m+c) Las Vegas algorithm, where n is the number of vertices of X and Y.read more
Citations
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Proceedings ArticleDOI
Faster isomorphism testing of strongly regular graphs
TL;DR: It is demonstrated that isomorphism of strongly regular graphs may be tested in time n in light of Neumaier’s claw bound, which implies that low degree stronglyRegular graphs have a small second-largest eigenvalue, unless they are Steiner or Latin square graphs.
Proceedings ArticleDOI
Isomorphism testing for embeddable graphs through definability
TL;DR: It is shown that for every surface S, there is a k _> 1 such that the k-dimensional WL-algori thm succeeds to decide isomorphism of graphs embeddable in S.
Proceedings ArticleDOI
Parallel algorithms for permutation groups and graph isomorphism
TL;DR: It is shown that NC contains isomorphism-testing for vertex-colored graphs with bounded color multiplicity, a problem not long known to be in polynomial time.
Journal ArticleDOI
Compact graphs and equitable partitions
TL;DR: In this article, the authors characterize the automorphism group of a compact regular graph and give a polynomial time algorithm for determining whether a regular graph on a prime number of vertices is compact.
Posted Content
Search Space Contraction in Canonical Labeling of Graphs
TL;DR: In this paper, the individualization-refinement paradigm for computing a canonical labeling and the automorphism group of a graph is investigated, and a new algorithmic design aimed at reducing the size of the associated search space is introduced.
References
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MonographDOI
Algebraic graph theory
TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.
Book
Spectra of graphs : theory and application
TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.
Proceedings ArticleDOI
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
John E. Hopcroft,J. K. Wong +1 more
TL;DR: The time bound for planar graph isomorphism is improved to O(|V|) time and the algorithm can be easily extended to partition a set of planar graphs into equivalence classes of isomorphic graphs in time linear in the total number of vertices in all graphs in the set.