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Enumeration of permanental sums of lattice graphs

Author

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  • Li, Wei
  • Qin, Zhongmei
  • Wang, Yao

Abstract

The permanental sum PS(G) is the coefficients sum of the permanental polynomial of a graph G. In this work, we exhibit the explicit expressions of the permanental sums of quadrilateral linear chains on the plane and quadrilateral linear rings on the cylinder by establishing orientation graphs, respectively. Meanwhile, we show that the permanental sum of the hexagonal linear chain with n hexagons is (n+1)2, which determines the value of permanental sum of the extremal hexagonal chain in [9].

Suggested Citation

  • Li, Wei & Qin, Zhongmei & Wang, Yao, 2020. "Enumeration of permanental sums of lattice graphs," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    • Handle: RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319309063
    DOI: 10.1016/j.amc.2019.124914
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    References listed on IDEAS

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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.
    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. 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. Wu, Tingzeng & Lai, Hong-Jian, 2018. "On the permanental sum of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 334-340.
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    Cited by:

    1. Bripi, Francesco & Bronzini, Raffaello & Gentili, Elena & Linarello, Andrea & Scarinzi, Elisa, 2024. "Structural change and firm dynamics in Southern Italy," Structural Change and Economic Dynamics, Elsevier, vol. 69(C), pages 678-691.

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