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Unicyclic graphs with second largest and second smallest permanental sums

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  • Wu, Tingzeng
  • So, Wasin

Abstract

Let A(G) be an adjacency matrix of a graph G. Then the polynomial π(G,x)=per(xI−A(G)) is called the permanental polynomial of G, and the permanental sum of G is the sum of the absolute values of the coefficients of π(G, x). In this paper, the second largest and second smallest permanental sums among connected unicyclic graphs and the corresponding extremal graphs are determined. In addition, we show that the computation of permanental sum is #P-complete.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:351:y:2019:i:c:p:168-175
    DOI: 10.1016/j.amc.2019.01.056
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    References listed on IDEAS

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    1. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.
    2. Li, Shuchao & Wei, Wei, 2018. "Extremal octagonal chains with respect to the coefficients sum of the permanental polynomial," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 45-57.
    3. Wu, Tingzeng & Lai, Hong-Jian, 2018. "On the permanental sum of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 334-340.
    4. 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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    Citations

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    Cited by:

    1. Tingzeng Wu & Huazhong Lü, 2019. "The Extremal Permanental Sum for a Quasi-Tree Graph," Complexity, Hindawi, vol. 2019, pages 1-4, May.
    2. 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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