Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (4): 379-387.doi: 10.13371/j.cnki.chin.q.j.m.2024.04.004

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Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs

  

  1. School of Information Engineering, Huzhou University, Huzhou 313000, China
  • Received:2024-05-04 Online:2024-12-30 Published:2024-12-30
  • Contact: ZHANG Ke (1986-), male, native of Dawu, Hubei, lecturer of Huzhou University, doctor, engages in complex networks and their applications; E-mail:hbsanli@163.com
  • About author:JI Lin-xing (2000-), female, native of Taizhou, Jiangsu, postgraduate student of Huzhou University, engages in complex networks and their applications; ZHANG Ke (1986-), male, native of Dawu, Hubei, lecturer of Huzhou University, doctor, engages in complex networks and their applications; HU Wen-jun (1977-), male, native of Jixi, Anhui, professor of Huzhou University, doctor, engages in machine learning and pattern recognition.
  • Supported by:
    Supported by National Natural Science Foundation of China (Grant No. U20A20228); Huzhou Science and Technology Plan Project (Grant No. 2022YZ53).

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Abstract: Research on the independence polynomial of graphs has been very active. However, the computational complexity of determining independence polynomials for general graphs remains NP-hard. Let α(G) be the independence number of G and i(G; k) be the number of independent sets of order k in G, then the independence polynomial is defined as ......

Key words: Independence polynomial, Cylindrical grid graphs, Transfer matrix; Merrifield-Simmons index

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