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Research Article

Fractional matching number and spectral radius of nonnegative matrices of graphs

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Pages 4133-4145 | Received 30 May 2020, Accepted 11 Dec 2020, Published online: 11 Jan 2021

References

  • Bondy JA, Murty USR. Graph theory GTM 244. New York (NY): Springer; 2008.
  • Nikiforov V. Merging the A-and Q-spectral theories. Appl Anal Discrete Math. 2017;11:81–107.
  • Scheinerman ER, Ullman DH. Fractional graph theory: a rational approach to the theory of graphs. New Jersey (NJ): Wiley & Sons; 1997.
  • Brouwer AE, Haemers WH. Eigenvalues and perfect matchings. Linear Algebra Appl. 2005;395:155–162.
  • Cioab SM. Perfect matchings eigenvalues and expansion. C R Math Acad Sci Soc R Can. 2005;27:101–104.
  • Cioab SM, Gregory DA. Large matchings from eigenvalues. Linear Algebra Appl. 2007;422:308–317.
  • Cioab SM, Gregory DA, Haemers WH. Matchings in regular graphs from eigenvalues. J Combin Theory Ser B. 2009;99:287–297.
  • O. S, Cioab SM Edge-connectivity eigenvalues and matchings in regular graphs. SIAM J Discrete Math. 2010;24:1470–1481.
  • O. S. Spectral radius and fractional matchings in graphs. European J Combin. 2016;55:144–148.
  • Xue J, Zhai MQ, Shu JL. Fractional matching number and eigenvalues of a graph. Linear Multilinear Algebra. 2019;67:2565–2574.
  • Hong YM, Gu XF, Lai H.-J, Liu QH, Fractional spanning tree packing forest covering and eigenvalues. Discrete Appl Math. 2016;213:219–223.
  • Liu QH, Hong YM, Lai H-J. Edge-disjoint spanning trees and eigenvalues. Linear Algebra Appl. 2014;444:146–151.
  • Liu QH, Hong YM, Gu XF, Lai H.-J, Note on edge-disjoint spanning trees and eigenvalues. Linear Algebra Appl. 2014;458:128–133.
  • Liu RF, Lai H-J, Tian YZ. Spanning tree packing number and eigenvalues of graphs with given girth. Linear Algebra Appl. 2019;578:411–424.
  • Liu RF, Lai H-J, Tian YZ, Wu. Y,Vertex-connectivity and eigenvalues of graphs with fixed girth. Appl Math Comput. 2019;344–345:141–149.
  • Dirac GA. Some theorems on abstract graphs. Proc London Math Soc. 1952;3:69–81.
  • Brouwer AE, Haemers WH. Spectra of graphs. New York (NY): Springer; 2012.
  • Haemers WH. Interlacing eigenvalues and graphs. Linear Algebra Appl. 1995;226-228:593–616.
  • Haynsworth EV. Applications of a theorem on partitioned matrices. J Res Natl Bur Stand. 1959;62:73–78.
  • You LH, Yang M, So W, Xi WG, On the spectrum of an equitable quotient matrix and its application. Linear Algebra Appl. 2019;577:21–40.
  • Berman A, Plemmons RJ. Nonnegative matrices in the mathematical sciences. New York (NY): Academic Press; 1979.
  • Horn RA, Johnson CR. Matrix analysis. New York (NY): Cambridge University Press; 1986.

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