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
Graph recurrence
TL;DR: Three concepts are defined: (1) for a graph to be determined by a set of vectors, (2) for two graphs to be m-equivalent, and (3) for the vertices of thegraph to be separated by aSet of vectors.
Posted Content
A Novel Framework for the Analysis of Unknown Transactions in Bitcoin: Theory, Model, and Experimental Results.
Maurantonio Caprolu,Matteo Pontecorvi,Matteo Signorini,Carlos David Pérez Segarra,Roberto Di Pietro +4 more
TL;DR: In this paper, the authors present a novel approach based on sound graph theory for identifying transaction inputs and outputs, which does not rely on BTC addresses and explores all the transactions stored in the blockchain.
Posted Content
Eigenvalue location in graphs of small clique-width
TL;DR: In this article, a diagonal matrix congruent to the adjacency matrix of a graph was found in time O(text{poly}(k) n) where n is the order of the graph's clique width.
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.