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Original Articles

Oriented bipartite graphs with minimal trace norm

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Pages 1121-1131 | Received 03 Jun 2017, Accepted 27 Feb 2018, Published online: 09 Mar 2018

References

  • Gutman I . The energy of a graph. Ber Math-Statist Sekt Forschungszentrum Graz. 1978;103:1–22.
  • Li X , Shi Y , Gutman I . Graph energy. New York (NY): Springer-Verlag; 2012.
  • Adiga C , Balakrishnan R , So W . The skew energy of a digraph. Linear Algebra Appl. 2010;432:1825–1835.
  • Peña I , Rada J . Energy of digraphs. Linear Multilinear Algebra. 2008;56:565–579.
  • Gutman I , Li X , editors. Energies of graphs -- theory and applications. Kragujevac: University of Kragujevac; 2016.
  • Nikiforov V . The energy of graphs and matrices. J Math Anal Appl. 2007;320:1472–1475.
  • Nikiforov V . Beyond graph energy: norms of graphs and matrices. Linear Algebra Appl. 2016;506:82–138.
  • Agudelo N , Rada J . Lower bounds of Nikiforov’s energy over digraphs. Linear Algebra Appl. 2016;496:156–164.
  • Agudelo N , de la Peña JA , Rada J . Extremal values of the trace norm over oriented trees. Linear Algebra Appl. 2016;505:261–268.
  • Day J , So W . Singular value inequality and graph energy change. Electron J Linear Algebra. 2007;16:291–299.
  • Fan K . Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc Nat Acad Sci USA. 1951;37:760–766.
  • Caporossi G , Cvetković D , Gutman I , et al . Variable neighborhood search for extremal graph. 2. Finding graphs with extremal energy. J Chem Inf Comput Sci. 1999;39:984–996.
  • Hou Y . Unicyclic graphs with minimal energy. J Math Chem. 2001;29:163–168.
  • Huo B , Li X . Complete solution to a conjecture on the maximal energy of unicyclic graphs. Eur J Combin. 2011;32:662–673.
  • Hou Y , Shen X , Zhang C . Oriented unicyclic graphs with extremal skew energy, arXiv:1108.6229v1 [math. CO].
  • Wang W-H . Ordering of oriented unicyclic graphs by skew energies. Appl Math Comput. 2016;284:136–148.
  • Zhu JM . Oriented unicyclic graphs with the first n−9/2 largest skew energies. Linear Algebra Appl. 2012;437:2630–2649.
  • Das K , Fritscher E , Pinheiro LK . Maximum Laplacian energy of unicyclic graphs. Discrete Appl Math. 2017;218:71–81.
  • Fritscher E , Hoppen C , Trevisan V . Unicyclic graphs with equal Laplacian energy. Linear Multilinear Algebra. 2014;62:180–194.
  • Gutman I . Graphs with greatest number of matchings. Publ Inst Math (Beograd). 1980;27:67–76.
  • Stevanović D , Ilić A . On the Laplacian coefficients of unicyclic graphs. Linear Algebra Appl. 2009;430:2290–2300.
  • Bozkurt ŞB , Güngör AD , Zhou B . Note on the distance energy of graphs. MATCH Commun Math Comput Chem. 2010;64:129–134.
  • Gutman I . Acyclic systems with extremal Hü ckel-electron energy. Theor Chim Acta. 1977;45:79–87.
  • Horn R , Johnson C . Matrix analysis. Cambridge: Cambridge University Press; 2013.

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