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Principal minor version of Matrix-Tree theorem for mixed graphs

Author

Listed:
  • Yu, Guihai
  • Qu, Hui
  • Dehmer, Matthias

Abstract

In Yu, et al. (2017), an analytical expression of the determinant of the Hermitian (quasi-)Laplacian matrix of mixed graphs has been proven. In this paper, we are going to extend those results and derive an analytical expression for the principal minors of the Hermitian (quasi-)Laplacian matrix, which is the principal minor version of the Matrix-Tree theorem.

Suggested Citation

  • Yu, Guihai & Qu, Hui & Dehmer, Matthias, 2017. "Principal minor version of Matrix-Tree theorem for mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 27-30.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:27-30
    DOI: 10.1016/j.amc.2017.03.034
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    References listed on IDEAS

    as
    1. Yu, Guihai & Qu, Hui, 2015. "Hermitian Laplacian matrix and positive of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 70-76.
    2. Yu, Guihai & Liu, Xin & Qu, Hui, 2017. "Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 287-292.
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