STUDY OF GRAPH ISOMORPHISM USING JORDAN FORMS OF ADJACENCY MATRICES

2018 ◽  
pp. 87-99
Author(s):  
M. I. Volodicheva ◽  
◽  
S. N. Leora ◽  
Keyword(s):  
Graph Isomorphism ◽  
Adjacency Matrices ◽  
Jordan Forms

scholarly journals Graph Cospectrality using Neighborhood Matrices

10.37236/2617 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Aline Duarte Bessa ◽  
Ivan Carmo Rocha-Neto ◽  
Suani Tavares Rubim de Pinho ◽  
Roberto Fernandes Silva Andrade ◽  
Thierry Correa Petit Lobao
Keyword(s):  
Graph Isomorphism ◽  
Higher Order ◽  
Matrix Representations ◽  
Signless Laplacian ◽  
Adjacency Matrices ◽  
Switching Method

In this note we address the problem of graph isomorphism by means of eigenvalue spectra of different matrix representations:  the neighborhood matrix $\hat{M}$, its corresponding signless Laplacian $Q_{\hat{M}}$, and the set of higher order adjacency matrices $M_{\ell}$s. We find that, in relation to graphs with at most 10 vertices, $Q_{\hat{M}}$ leads to better results than the signless Laplacian $Q$; besides, when combined with $\hat{M}$, it even surpasses the Godsil and McKay switching method.

scholarly journals Quantum walks defined by digraphs and generalized Hermitian adjacency matrices

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Sho Kubota ◽  
Etsuo Segawa ◽  
Tetsuji Taniguchi
Keyword(s):  
Quantum Walks ◽  
Adjacency Matrices

scholarly journals Research on Blockchain-Based E-Bidding System

2021 ◽  
Vol 11 (9) ◽  
pp. 4011
Author(s):  
Dan Wang ◽  
Jindong Zhao ◽  
Chunxiao Mu
Keyword(s):  
Data Transmission ◽  
Privacy Protection ◽  
Graph Isomorphism ◽  
Third Party ◽  
Business Logic ◽  
Core Concept ◽  
The Core ◽  
Blockchain Technology ◽  
Smart Contract ◽  
Bidding Process

In the field of modern bidding, electronic bidding leads a new trend of development, convenience and efficiency and other significant advantages effectively promote the reform and innovation of China’s bidding field. Nowadays, most systems require a strong and trusted third party to guarantee the integrity and security of the system. However, with the development of blockchain technology and the rise of privacy protection, researchers has begun to emphasize the core concept of decentralization. This paper introduces a decentralized electronic bidding system based on blockchain and smart contract. The system uses blockchain to replace the traditional database and uses chaincode to process business logic. In data interaction, encryption techniques such as zero-knowledge proof based on graph isomorphism are used to improve privacy protection, which improves the anonymity of participants, the privacy of data transmission, and the traceability and verifiable of data. Compared with other electronic bidding systems, this system is more secure and efficient, and has the nature of anonymous operation, which fully protects the privacy information in the bidding process.

scholarly journals Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1522
Author(s):  
Anna Concas ◽  
Lothar Reichel ◽  
Giuseppe Rodriguez ◽  
Yunzi Zhang
Keyword(s):  
Iterative Methods ◽  
Adjacency Matrix ◽  
Lanczos Method ◽  
Power Method ◽  
Arnoldi Method ◽  
Multiple Eigenvalues ◽  
Computer Storage ◽  
Adjacency Matrices ◽  
Lanczos Methods ◽  
Perron Vector

The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude. It is well known that the Lanczos method typically requires fewer iterations than the power method to determine eigenvectors with the desired accuracy. However, the Lanczos method demands more computer storage, which may make it impractical to apply to very large problems. The present paper adapts the analysis by Blondel et al. to the Lanczos and restarted Lanczos methods. The restarted methods are found to yield fast convergence and to require less computer storage than the Lanczos method. Computed examples illustrate the theory presented. Applications of the Arnoldi method are also discussed.

scholarly journals MET: a Java package for fast molecule equivalence testing

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Jördis-Ann Schüler ◽  
Steffen Rechner ◽  
Matthias Müller-Hannemann
Keyword(s):  
Chemical Properties ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Equivalence Classes ◽  
Equivalence Testing ◽  
Equivalence Test ◽  
Graph Isomorphism Problem ◽  
2D Structure ◽  
Node Labels ◽  
Labelled Graphs

AbstractAn important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.

scholarly journals Graph isomorphism restricted by lists

2021 ◽  
Vol 860 ◽  
pp. 51-71
Author(s):  
Pavel Klavík ◽  
Dušan Knop ◽  
Peter Zeman
Keyword(s):  
Graph Isomorphism
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