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Computing the permanental polynomials of graphs

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  • Liu, Xiaogang
  • Wu, Tingzeng

Abstract

Let M be an n × n matrix with entries mij (i,j=1,2,…,n). The permanent of M is defined to be per(M)=∑σ∏i=1nmiσ(i),where the sum is taken over all permutations σ of {1,2,…,n}. The permanental polynomial of M is defined by per(xIn−M), where In is the identity matrix of size n. In this paper, we give recursive formulas for computing permanental polynomials of the Laplacian matrix and the signless Laplacian matrix of a graph, respectively.

Suggested Citation

  • Liu, Xiaogang & Wu, Tingzeng, 2017. "Computing the permanental polynomials of graphs," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 103-113.
    • Handle: RePEc:eee:apmaco:v:304:y:2017:i:c:p:103-113
    DOI: 10.1016/j.amc.2017.01.052
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    Cited by:

    1. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.
    2. Wu, Tingzeng & Zhou, Tian & Lü, Huazhong, 2022. "Further results on the star degree of graphs," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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