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On the permanental sum of graphs

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  • Wu, Tingzeng
  • Lai, Hong-Jian

Abstract

Let G be a graph and A(G) the adjacency matrix of G. The polynomial π(G,x)=per(xI−A(G)) is called the permanental polynomial of G, and the permanental sum of G is the summation of the absolute values of the coefficients of π(G, x). In this paper, we investigate properties of permanental sum of a graph, prove recursive formulas to compute the permanental sum of a graph, and show that the ordering of graphs with respect to permanental sum. Furthermore, we determine the upper and lower bounds of permanental sum of unicyclic graphs, and the corresponding extremal unicyclic graphs are also determined.

Suggested Citation

  • Wu, Tingzeng & Lai, Hong-Jian, 2018. "On the permanental sum of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 334-340.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:334-340
    DOI: 10.1016/j.amc.2018.03.026
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    References listed on IDEAS

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    1. Li, Wei & Qin, Zhongmei & Zhang, Heping, 2016. "Extremal hexagonal chains with respect to the coefficients sum of the permanental polynomial," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 30-38.
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    Cited by:

    1. Li, Wei & Qin, Zhongmei & Wang, Yao, 2020. "Enumeration of permanental sums of lattice graphs," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    2. Tingzeng Wu & Huazhong Lü, 2019. "The Extremal Permanental Sum for a Quasi-Tree Graph," Complexity, Hindawi, vol. 2019, pages 1-4, May.
    3. Wu, Tingzeng & So, Wasin, 2019. "Unicyclic graphs with second largest and second smallest permanental sums," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 168-175.
    4. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.

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    1. Tingzeng Wu & Huazhong Lü, 2019. "The Extremal Permanental Sum for a Quasi-Tree Graph," Complexity, Hindawi, vol. 2019, pages 1-4, May.
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    5. Li, Wei & Qin, Zhongmei & Wang, Yao, 2020. "Enumeration of permanental sums of lattice graphs," Applied Mathematics and Computation, Elsevier, vol. 370(C).

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