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Enumeration of cospectral and coinvariant graphs

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Abstract
We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (cospectral mate), or at least one other graph with the same Smith normal form (coinvariant mate) with respect to several matrices associated to a graph. The presented numerical data give some indication that possibly the Smith normal form of the distance Laplacian and the signless distance Laplacian matrices could be a finer invariant than the spectrum to distinguish graphs. Finally, we prove a graph characterization using the Smith normal form of the distance signless Laplacian matrix.
Keywords
Applied Mathematics, Computational Mathematics, Graph invariant, Eigenvalues, Invariant factors, Smith normal form, Enumeration, DISTANCE, LAPLACIANS

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MLA
Abiad, Aida, and Carlos A. Alfaro. “Enumeration of Cospectral and Coinvariant Graphs.” APPLIED MATHEMATICS AND COMPUTATION, vol. 408, 2021, doi:10.1016/j.amc.2021.126348.
APA
Abiad, A., & Alfaro, C. A. (2021). Enumeration of cospectral and coinvariant graphs. APPLIED MATHEMATICS AND COMPUTATION, 408. https://doi.org/10.1016/j.amc.2021.126348
Chicago author-date
Abiad, Aida, and Carlos A. Alfaro. 2021. “Enumeration of Cospectral and Coinvariant Graphs.” APPLIED MATHEMATICS AND COMPUTATION 408. https://doi.org/10.1016/j.amc.2021.126348.
Chicago author-date (all authors)
Abiad, Aida, and Carlos A. Alfaro. 2021. “Enumeration of Cospectral and Coinvariant Graphs.” APPLIED MATHEMATICS AND COMPUTATION 408. doi:10.1016/j.amc.2021.126348.
Vancouver
1.
Abiad A, Alfaro CA. Enumeration of cospectral and coinvariant graphs. APPLIED MATHEMATICS AND COMPUTATION. 2021;408.
IEEE
[1]
A. Abiad and C. A. Alfaro, “Enumeration of cospectral and coinvariant graphs,” APPLIED MATHEMATICS AND COMPUTATION, vol. 408, 2021.
@article{8712522,
  abstract     = {{We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (cospectral mate), or at least one other graph with the same Smith normal form (coinvariant mate) with respect to several matrices associated to a graph. The presented numerical data give some indication that possibly the Smith normal form of the distance Laplacian and the signless distance Laplacian matrices could be a finer invariant than the spectrum to distinguish graphs. Finally, we prove a graph characterization using the Smith normal form of the distance signless Laplacian matrix.}},
  articleno    = {{126348}},
  author       = {{Abiad, Aida and Alfaro, Carlos A.}},
  issn         = {{0096-3003}},
  journal      = {{APPLIED MATHEMATICS AND COMPUTATION}},
  keywords     = {{Applied Mathematics,Computational Mathematics,Graph invariant,Eigenvalues,Invariant factors,Smith normal form,Enumeration,DISTANCE,LAPLACIANS}},
  language     = {{eng}},
  pages        = {{9}},
  title        = {{Enumeration of cospectral and coinvariant graphs}},
  url          = {{http://dx.doi.org/10.1016/j.amc.2021.126348}},
  volume       = {{408}},
  year         = {{2021}},
}

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