On the Limitations of Graph Invariants Inspired by Quantum Walks

Electronic Notes in Discrete Mathematics

Volumn 38, Issue , 2011, Pages 795-801

  Smith, Jamie ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Cellular algebras; Graph isomorphism problem; Quantum walks

Indexed keywords

EID: 82955219764     PISSN: None     EISSN: 15710653     Source Type: Journal    
DOI: 10.1016/j.endm.2011.10.033     Document Type: Article

References (9)

1. Leman A.A., Weisfeiler B.Yu. A reduction of a graph to a canonical form and an algebra arising during this reduction. Nauchno-Techn. Inform. Ser. 1968, 2(9):12-16.
2. Cai J., Fürer M., Immerman N. An optimal lower bound on the number of variables for graph identification. Combinatorica Jan 1992.
3. Emms David, Hancock Edwin R., Severini Simone, Wilson Richard C. A matrix representation of graphs and its spectrum as a graph invariant arxiv:quant-ph/0505026v2.
4. Evdokimov Sergei, Karpinski Marek, Ponomarenko Ilia On a new high dimensional weisfeiler-lehman algorithm. J. Algebraic Comb. July 1999, 10:29-45.
5. Gamble John King, Friesen Mark, Zhou Dong, Joynt Robert, Coppersmith S.N. Two-particle quantum walks applied to the graph isomorphism problem. Phys. Rev. A May 2010, 81.
6. Godsil Chris, Guo Krystal Quantum walks on regular graphs and eigenvalues arxiv:1011.5460v1.
7. Ilya Ponomarenko and Amir Barghi. Non-isomorphic graphs with cospectral symmetric powers. pages 1-14, Sep 2009.
8. Smith J. k-boson quantum walks do not distinguish arbitrary graphs Arxiv preprint. arxiv:1004.0206.
9. Smith J. Cellular algebras and graph invariants based on quantum walks Arxiv preprint. arxiv:1103.0262.