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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Finding Small Weight Isomorphisms with Additional Constraints is Fixed-Parameter Tractable
TL;DR: The problem of deciding whether there is an isomorphism between two graphs that moves k vertices and satisfies Lubiw-style constraints is in FPT, with k and the size of $R$ as parameters.
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On Graph Isomorphism Problem
TL;DR: In this article, the problem of determining whether or not two given graphs are isomorphic is called Graph Isomorphism Problem (GI) is reduced to that of working out a series of partitions of a stabilizer that fixes a sequence of vertices of a given graph.
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On the Automorphism Group of a Graph
TL;DR: In this paper, a permutation representation of the automorphism of a graph G is given in the form of a bijective map, where the structure of the action is represented by its block systems.
Proceedings ArticleDOI
Joint Graph Embedding and Alignment with Spectral Pivot
TL;DR: In this article, an alternating optimization algorithm is proposed for computing high-quality approximate solutions and compared against the prevailing state-of-the-art graph aligning frameworks using benchmark real-world graphs.
Journal ArticleDOI
Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model
Manuel Igelmo,Alberto Sanfeliu +1 more
TL;DR: This paper presents a new method of filtering graphs to check exact graph isomorphism and extracting their mapping, and its application to detect isomorphic graphs in two well know graph databases, where some graphs have more than 600 nodes.
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.