IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v339y2018icp38-44.html
   My bibliography  Save this article

The coefficients of the immanantal polynomial

Author

Listed:
  • Yu, Guihai
  • Qu, Hui

Abstract

An expression of the coefficient of immanantal polynomial of an n × n matrix is present. Moreover, we give expressions of the coefficient of immanantal polynomials of combinatorial matrices (adjacency matrix, Laplacian matrix, signless Laplacian matrix). As applications, we show that the immanantal polynomials for Laplacian matrix and signless Laplacian matrix of bipartite graphs are the same. This is a generalization of the characteristic polynomial for Laplacian matrix and signless Laplacian matrix of bipartite graphs. Furthermore, we consider the relations between the characteristic polynomial and the immanantal polynomial for trees.

Suggested Citation

  • Yu, Guihai & Qu, Hui, 2018. "The coefficients of the immanantal polynomial," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 38-44.
  • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:38-44
    DOI: 10.1016/j.amc.2018.06.057
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318305460
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.06.057?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cao, Shujuan & Dehmer, Matthias & Kang, Zhe, 2017. "Network Entropies Based on Independent Sets and Matchings," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 265-270.
    2. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    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. Lan, Yongxin & Li, Tao & Ma, Yuede & Shi, Yongtang & Wang, Hua, 2018. "Vertex-based and edge-based centroids of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 445-456.
    5. Liu, Xiaogang & Wu, Tingzeng, 2017. "Computing the permanental polynomials of graphs," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 103-113.
    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. Tingzeng Wu & Huazhong Lü, 2019. "The Extremal Permanental Sum for a Quasi-Tree Graph," Complexity, Hindawi, vol. 2019, pages 1-4, May.
    2. 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.
    3. 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).
    4. Wu, Tingzeng & Zhou, Tian & Lü, Huazhong, 2022. "Further results on the star degree of graphs," Applied Mathematics and Computation, Elsevier, vol. 425(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. Ma, Yuede & Cao, Shujuan & Shi, Yongtang & Dehmer, Matthias & Xia, Chengyi, 2019. "Nordhaus–Gaddum type results for graph irregularities," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 268-272.
    2. Cai, Qingqiong & Cao, Fuyuan & Li, Tao & Wang, Hua, 2018. "On distances in vertex-weighted trees," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 435-442.
    3. Lan, Yongxin & Li, Tao & Ma, Yuede & Shi, Yongtang & Wang, Hua, 2018. "Vertex-based and edge-based centroids of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 445-456.
    4. Li, Yinkui & Gu, Ruijuan, 2018. "Bounds for scattering number and rupture degree of graphs with genus," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 329-334.
    5. Tratnik, Niko, 2018. "On the Steiner hyper-Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 360-371.
    6. Lan, Yongxin & Li, Tao & Wang, Hua & Xia, Chengyi, 2019. "A note on extremal trees with degree conditions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 70-79.
    7. Tingzeng Wu & Huazhong Lü, 2019. "The Extremal Permanental Sum for a Quasi-Tree Graph," Complexity, Hindawi, vol. 2019, pages 1-4, May.
    8. Noureen, Sadia & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2021. "Towards the solution of an extremal problem concerning the Wiener polarity index of alkanes," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    9. Li, Fengwei & Ye, Qingfang & Broersma, Hajo & Ye, Ruixuan & Zhang, Xiaoyan, 2021. "Extremality of VDB topological indices over f–benzenoids with given order," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    10. Wang, Juan & Li, Chao & Xia, Chengyi, 2018. "Improved centrality indicators to characterize the nodal spreading capability in complex networks," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 388-400.
    11. Ghorbani, Modjtaba & Dehmer, Matthias & Rajabi-Parsa, Mina & Emmert-Streib, Frank & Mowshowitz, Abbe, 2019. "Hosoya entropy of fullerene graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 88-98.
    12. Liu, Xiaoxiao & Sun, Shiwen & Wang, Jiawei & Xia, Chengyi, 2019. "Onion structure optimizes attack robustness of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    13. 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.
    14. Wan, Pengfei & Tu, Jianhua & Dehmer, Matthias & Zhang, Shenggui & Emmert-Streib, Frank, 2019. "Graph entropy based on the number of spanning forests of c-cyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    15. Li, Shuchao & Wang, Hua & Wang, Shujing, 2019. "Some extremal ratios of the distance and subtree problems in binary trees," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 232-245.
    16. Li, Wei & Qin, Zhongmei & Wang, Yao, 2020. "Enumeration of permanental sums of lattice graphs," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    17. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    18. Ali, Akbar & Du, Zhibin & Ali, Muhammad, 2018. "A note on chemical trees with minimum Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 231-236.
    19. Wan, Pengfei & Tu, Jianhua & Zhang, Shenggui & Li, Binlong, 2018. "Computing the numbers of independent sets and matchings of all sizes for graphs with bounded treewidth," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 42-47.
    20. Mikołaj Morzy & Tomasz Kajdanowicz & Przemysław Kazienko, 2017. "On Measuring the Complexity of Networks: Kolmogorov Complexity versus Entropy," Complexity, Hindawi, vol. 2017, pages 1-12, November.

    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:eee:apmaco:v:339:y:2018:i:c:p:38-44. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.