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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DissertationDOI
A Riemann-Roch Theory for Sublattices of the Root Lattice A n, Graph Automorphisms and Counting Cycles in Graphs
TL;DR: A geometric proof of the Riemann-Roch theorem for graphs is obtained and an algorithm for the related problem of counting automorphisms of graphs that is based on exponential sums is obtained.
Posted Content
Automorphism groups of maps in linear time
TL;DR: This work presents a linear-time algorithm for computing the generators of the automorphism group of a map, parametrized by the genus of the underlying surface, and extends the algorithm to non-orientable surfaces by making use of the antipodal double-cover.
DissertationDOI
Generation of Graph Classes with Efficient Isomorph Rejection
TL;DR: In this paper, an efficient isomorph-free generation of graph classes with the method of generation by canonical construction path (GCCP) is discussed, which is a general method to recursively generate combinatorial objects avoiding isomorphic copies.
Book ChapterDOI
Graph Isomorphism Algorithm by Perfect Matching
Kazuma Fukuda,Mario Nakamori +1 more
TL;DR: This paper determined graph isomorphism with the help of perfect matching algorithm, to limit the range of search of 1 to 1 correspondences between the two graphs to information in the table, and obtained a complextity of O(n 4).
Book ChapterDOI
Graph Isomorphism Restricted by Lists
TL;DR: The complexity of graph isomorphism (GraphIso) is a famous problem in computer science as mentioned in this paper, and it asks whether they are the same up to a relabeling of vertices.
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.