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The Extremal Permanental Sum for a Quasi-Tree Graph

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  • Tingzeng Wu
  • Huazhong Lü

Abstract

Let be a graph and the adjacency matrix of . The permanent of matrix is called the permanental polynomial of . The permanental sum of is the sum of the absolute values of the coefficients of permanental polynomial of . Computing the permanental sum is #p-complete. In this note, we prove the maximum value and the minimum value of permanental sum of quasi-tree graphs. And the corresponding extremal graphs are also determined. Furthermore,we also determine the graphs with the minimum permanental sum among quasi-tree graphs of order and size , where .

Suggested Citation

  • Tingzeng Wu & Huazhong Lü, 2019. "The Extremal Permanental Sum for a Quasi-Tree Graph," Complexity, Hindawi, vol. 2019, pages 1-4, May.
    • Handle: RePEc:hin:complx:4387650
    DOI: 10.1155/2019/4387650
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    References listed on IDEAS

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    1. Wu, Tingzeng & Lai, Hong-Jian, 2018. "On the permanental sum of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 334-340.
    2. 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.
    3. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.
    4. 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.
    5. 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.
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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).

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