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.