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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Journal ArticleDOI
Separation index of a graph
TL;DR: In this article, the separation index of a graph and of a surface has been shown to be at most 3, and it is shown that any graph faithfully embedded in a surface of genus g is bounded by a funtion of g.
Journal ArticleDOI
Eigenvalue location in graphs of small clique-width
TL;DR: In this paper, a diagonal matrix congruent to A − c I for constants c, where A is the adjacency matrix of a graph G allows us to quickly tell the number of eigenvalues in a given interval.
Book ChapterDOI
Fast digital signature algorithm based on subgraph isomorphism
TL;DR: The purpose is to provide very fast signature creation for embedded systems at the cost of somewhat longer signatures, and to analyze a class of problems that are based on graph theoretic problems instead of modular arithmetics.
Journal ArticleDOI
Graph isomorphism and Gaussian boson sampling
TL;DR: In this article, a Gaussian boson sampler is used to encode graphs into quantum states of light, whose properties are then probed with photon-number-resolving detectors.
Posted Content
On the Complexity of Matroid Isomorphism Problem
TL;DR: It is able to show that graphic matroid isomorphism testing for planar graphs can be done in deterministic polynomial time, and it is proved that the automorphism problems are polynomially time equivalent to the corresponding isomorphic problems.
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.