IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4387650.html
   My bibliography  Save this article

The Extremal Permanental Sum for a Quasi-Tree Graph

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/4387650.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/4387650.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/4387650?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Li, Wei & Qin, Zhongmei & Wang, Yao, 2020. "Enumeration of permanental sums of lattice graphs," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    3. 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.
    4. Zhai, Shaohui & Alrowaili, Dalal & Ye, Dong, 2018. "Clar structures vs Fries structures in hexagonal systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 384-394.
    5. Wu, Tingzeng & Lai, Hong-Jian, 2018. "On the permanental sum of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 334-340.
    6. Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.
    7. Wu, Tingzeng & Yu, Yong & Gao, Xing, 2023. "The second immanantal polynomials of Laplacian matrices of unicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    8. Wu, Tingzeng & Zhou, Tian & Lü, Huazhong, 2022. "Further results on the star degree of graphs," Applied Mathematics and Computation, Elsevier, vol. 425(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:4387650. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.