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

JI Lin-xing, ZHANG Ke, HU Wen-jun

doi:10.13371/j.cnki.chin.q.j.m.2024.04.004

Chinese Quarterly Journal of Mathematics >

2024 , Vol. 39 >Issue 4: 379 - 387

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.04.004

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

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School of Information Engineering, Huzhou University, Huzhou 313000, China

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.

Received date: 2024-05-04

Online published: 2024-12-30

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

Cite this article

JI Lin-xing, ZHANG Ke, HU Wen-jun . Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(4) : 379 -387 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.004

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