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On the Trace Norms of Orientations of Graphs

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Abstract

The trace norm of the digraph is defined as the sum of the singular values of its adjacency matrix. We determine the orientations with, respectively, small and large trace norms among orientations of trees and unicyclic graphs, respectively.

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References

  1. Agudelo, N., de la Peña, J.A., Rada, J.: Extremal values of the trace norm over oriented trees. Linear Algebra Appl. 505, 261–268 (2016)

    Article  MathSciNet  Google Scholar 

  2. Agudelo, N., Rada, J.: Lower bounds of Nikiforov’s energy over digraphs. Linear Algebra Appl. 496, 156–164 (2016)

    Article  MathSciNet  Google Scholar 

  3. Agudelo, N., Rada, J., Rivera, M.: Upper bound for the trace norm of the Laplacian matrix of a digraph and normally regular digraphs. Linear Algebra Appl. 552, 194–209 (2018)

    Article  MathSciNet  Google Scholar 

  4. Gutman, I.: The energy of a graph. Ber. Math.-Stat. Sekt. Forsch. Graz 103, 1–22 (1978)

    MATH  Google Scholar 

  5. Horn, R., Johnson, C.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)

    Book  Google Scholar 

  6. Hou, Y.: Unicyclic graphs with minimal energy. J. Math. Chem. 29, 163–168 (2001)

    Article  MathSciNet  Google Scholar 

  7. Kharaghani, H., Tayfeh-Rezaie, B.: On the energy of \((0, 1)\)-matrices. Linear Algebra Appl. 429, 2046–2051 (2008)

    Article  MathSciNet  Google Scholar 

  8. Li, X., Shi, Y., Gutman, I.: Graph Energy. Springer, New York (2012)

    Book  Google Scholar 

  9. Monsalve, J., Rada, J.: Oriented bipartite graphs with minimal trace norm. Linear Multilinear Algebra 67, 1121–1131 (2019)

    Article  MathSciNet  Google Scholar 

  10. Monsalve, J., Rada, J., Shi, Y.: Extremal values of energy over oriented bicyclic graphs. Appl. Math. Comput. 342, 26–34 (2019)

    MathSciNet  MATH  Google Scholar 

  11. Nikiforov, V.: The trace norm of \(r\)-partite graphs and matrices. C. R. Math. Acad. Sci. Paris 353, 471–475 (2015)

    Article  MathSciNet  Google Scholar 

  12. Nikiforov, V.: The energy of graphs and matrices. J. Math. Anal. Appl. 326, 1472–1475 (2007)

    Article  MathSciNet  Google Scholar 

  13. Nikiforov, V., Agudelo, N.: On the minimum trace norm/energy of \((0,1)\)-matrices. Linear Algebra Appl. 526, 42–59 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 11701102) and Guangdong Provincial Natural Science Foundation of China (Nos. 2017A030310441 and 2017A030313032).

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Authors and Affiliations

  1. Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510090, People’s Republic of China

    Jianping Li

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Bo Zhou

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  1. Jianping Li
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  2. Bo Zhou
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Correspondence to Bo Zhou.

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Communicated by Sanming Zhou.

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Li, J., Zhou, B. On the Trace Norms of Orientations of Graphs. Bull. Malays. Math. Sci. Soc. 43, 3513–3528 (2020). https://doi.org/10.1007/s40840-019-00881-y

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  • DOI: https://doi.org/10.1007/s40840-019-00881-y

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