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Power Series and Inequalities on the Parameters of a Strongly Regular Graph

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Innovations in Industrial Engineering II (icieng 2022)

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Abstract

In the following, we deal with the problem of the existence of primitive strongly regular graphs with 1 in its spectrum and such that its regularity is between certain values with respect to the order of the graph. We consider the natural correspondence between the adjacency matrix of a strongly regular graph and the Euclidean Jordan algebra, \(\mathcal {B}\), generated by the natural powers of that matrix. Considering the spectrum of a constructed series of Hadamard powers an element of that Euclidean Jordan algebra \({\mathcal B}\), we establish a necessary condition for the existence of this kind of primitive strongly regular graphs.

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References

  1. Diestel, R.: Graph Theory. Springer, Berlin (2000)

    Google Scholar 

  2. Jacobson, N.: Structure and Representation of Jordan Algebras, volume \(XXXIX\) of Colloquium Publications American Mathematical Society, Providence, Rhode Island (1968)

    Google Scholar 

  3. Koecher, M.: The Minnesota Notes on Jordan Algebras and Their Applications. Springer, Heidelberg (1999). https://doi.org/10.1007/BFb0096285

    Book  MATH  Google Scholar 

  4. McCrimmon, K.: A Taste of Jordan Algebras. Springer, New York (2003). https://doi.org/10.1007/b97489

    Book  MATH  Google Scholar 

  5. Faraut, J., Korányi, A.: Analysis on Symmetric Cones. Oxford Mathematical Monographs, Clarendon Press, Oxford (1994)

    MATH  Google Scholar 

  6. Faybusovich, L.: Euclidean Jordan algebras and interior point algorithms. Positivity 1(4), 331–357 (1997)

    Article  MathSciNet  Google Scholar 

  7. Faybusovich, L.: Linear systems in Jordan algebras and primal dual interior point algorithms. J. Comput. Appl. Math. 86, 149–175 (1997)

    Article  MathSciNet  Google Scholar 

  8. Faybusovich, L.: A Jordan algebraic approach to potential redution algorithms. Mathematitische Zeitschrift 239, 117–129 (2002)

    Article  Google Scholar 

  9. Gowda, M.S., Sznajder, R.S.: Schur complements, Schur determinenatal and Haynsworth inertia formulas in Euclidean Jordan algebras. Linear Algebra Appl. 432, 1553–1559 (2010)

    Article  MathSciNet  Google Scholar 

  10. Gowda, M.S., Sznadjer, R.S., Tao, J.: Some P properties for linear transformations on Euclidean Jordan algebras. Linear Algebra Appl. 393, 203–232 (2004)

    Article  MathSciNet  Google Scholar 

  11. Vieira, L.A.: Euclidean Jordan algebras and inequalities over the spectrum of a strongly regular graph. J. Phys.: Conf. Ser. 1564, 1–10 (2020)

    Google Scholar 

  12. Vieira, L.A.: Generalized inequalities associated to the regularity of a strongly regular graph. J. Comput. Methods Sci. Eng. 19(3), 673–680 (2019)

    Google Scholar 

  13. Cardoso, D.M., Vieira, L.A.: On the optimal parameter of a self-concordant barrier over a symmetric cone. Eur. J. Oper. Res. 169, 1148–1157 (2006)

    Article  MathSciNet  Google Scholar 

  14. Helmke, U., Ricardo, S., Yoshizawa, S.: Newton’s algorithm in Euclidean Jordan algebras with applications to robotics. Commun. Inf. Syst. 2(3), 283–298 (2002)

    Article  MathSciNet  Google Scholar 

  15. Baes, M.: Spectral functions and smoothing techniques on Jordan algebras. Ph.D. Thesis, University Catholique of Louvain (2006)

    Google Scholar 

  16. Schmieta, S.H.: Application of Jordan algebras to the design and analysis of interior point algorithms for linear, quadratically constrained quadratic, and semi definite programming. Ph.D. thesis, Rutgers University (1999)

    Google Scholar 

  17. Vieira, M.V.C.: Jordan algebraic approach to symmetric optimization. Ph.D. thesis, Technische Universiteit Delft (2007)

    Google Scholar 

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Acknowledgments

In this work Luís Vieira was partially supported by the Center of Research of Mathematics of University of Porto (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.

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Authors and Affiliations

  1. Faculty of Engineering of Porto, Section of Mathematics, Porto, Portugal

    Luís Almeida Vieira

  2. University of Porto, Center of Mathematics of University of Porto, Porto, Portugal

    Luís Almeida Vieira

  3. University of Porto, Porto, Portugal

    Vasco Moço Mano

Authors
  1. Luís Almeida Vieira
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  2. Vasco Moço Mano
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Corresponding author

Correspondence to Luís Almeida Vieira .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Minho, Guimarães, Portugal

    José Machado

  2. Department of Industrial Electronics, University of Minho, Guimarães, Portugal

    Filomena Soares

  3. Poznan University of Technology, Poznan, Wielkopolskie, Poland

    Justyna Trojanowska

  4. Department of Manufacturing Engineering, Machines and Tools, Sumy State University, Sumy, Ukraine

    Vitalii Ivanov

  5. Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Rzeszow, Poland

    Katarzyna Antosz

  6. School of Reliability and Systems Engineering, Beihang University, Beijing, China

    Yi Ren

  7. Department of Mechanical Engineering, National Institute of Technology Waranga, Hanamkonda, India

    Vijaya Kumar Manupati

  8. Faculty of Industrial Engineering, University of Vigo, Galicia, Pontevedra, Spain

    Alejandro Pereira

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Vieira, L.A., Mano, V.M. (2023). Power Series and Inequalities on the Parameters of a Strongly Regular Graph. In: Machado, J., et al. Innovations in Industrial Engineering II. icieng 2022. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-09360-9_8

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  • DOI: https://doi.org/10.1007/978-3-031-09360-9_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09359-3

  • Online ISBN: 978-3-031-09360-9

  • eBook Packages: EngineeringEngineering (R0)

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