Matching Polynomials and Independence Polynomials of Hexacyclic Systems

Document Type : Research Paper

Author

School of Mathematics‎, ‎Changsha University‎, ‎Changsha 410022‎, ‎P‎. ‎R‎. ‎China

10.22052/ijmc.2025.257868.2080

Abstract

‎It is well established that matching and independence polynomials hold great significance in mathematical chemistry‎, ‎serving as core tools to bridge the topological features of molecular graphs with quantifiable chemical properties‎. ‎Against this backdrop‎, ‎this paper focuses on computing the matching and independence polynomials of both hexacyclic systems and their M\"{o}bius counterparts‎. ‎Building upon the research presented in Matching polynomials and independence polynomials of benzenoid chains [\textit{MATCH Commun‎. ‎Math‎. ‎Comput‎. ‎Chem.} \textbf{92} (2024) 779-809]‎, ‎we first develop methods to determine the matching and independence polynomials for an arbitrary hexacyclic system $F_{\vartheta_1\vartheta_2\cdots\vartheta_{h}}$ and its M\"{o}bius counterpart $M_{\vartheta_1\vartheta_2\cdots\vartheta_{h}}$‎. ‎Subsequently‎, ‎computational formulas for the Hosoya index and Merrifield-Simmons index of both systems are derived‎.

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References

[1] G. H. Fath-Tabar and A. Loghman, On vertex matching polynomial of graphs, Ars Combin. 104 (2012) 375–384.
[2] F. Taghvaee and G. H. Fath-Tabar, Relationship between coefficients of characteristic polynomial and matching polynomial of regular graphs and its applications, Iranian J. Math. Chem. 8 (2017) 7–23, https://doi.org/10.22052/IJMC.2017.15093.
[3] Y. Shi, M. Dehmer, X. Li and I. Gutman, Graph Polynomials, CRC Press, Boca Raton, 2016.
[4] E. J. Farrel, An introduction to matching polynomials, J. Combin. Theory Ser. 27 (1979) 75–86, https://doi.org/10.1016/0095-8956(79)90070-4.
[5] L. Lovasz and M. D. Plummer, Mathing theory, Annals of Discrete Mathematics, Vol 9 (North-Holland, Amsterdam) 1986.
[6] I. Gutman and F. Harary, Generalizations of the matching polynomial, Utilitas Math. 24 (1983) 97–106.
[7] H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971) 2332–2339.
[8] T. M.Westerberg, K. J. Dawson and K. W. McLaughlin, The Hosoya index, Lucas numbers and QSPR, Endeavor (University of Wisconsin-River Falls), 1 (2005) 1–15.
[9] R. E. Merrifield and H. E. Simmons, The structure of molecular topological space, Theor. Chem Acta 55 (1980) 55–75.
[10] H. Chen, X. Liu and J. Shen, Matching polynomials and independence polynomials of benzenoid chains, MATCH Commun. Math. Comput. Chem. 92 (2024) 779–809, https://doi.org/10.46793/match.92-3.779C.
[11] M. S. Oz and I. N. Cangul, Computing the number of k-matchings in benzenoid chains, MATCH Commun. Math. Comput. Chem. 88 (2022) 79–92, https://doi.org/10.46793/match.88-1.079O.
[12] M. S. Oz and I. N. Cangul, Enumeration of independent sets in benzenoid chains, MATCH Commun. Math. Comput. Chem. 88 (2022) 93–107, https://doi.org/10.46793/match.88-1.093O.
[13] H. Chen and X. Gao, Computing the matching polynomials and independence polynomials of phenylene chains, Int. J. Quantum Chem. 125 (2025) #e70002, https://doi.org/10.1002/qua.70002.
[14] H. Chen, Q. Guo and Y. Tan, Computing the matching and independence polynomials of double hexagonal chains, Discrete Appl. Math. 363 (2025) 139–157, https://doi.org/10.1016/j.dam.2024.12.006.
[15] M. S. Oz, R. Cruz and J. Rada, Computation method of the Hosoya index of primitive coronoid systems, Math. Biosci. Eng. 19 (2022) 9842–9852, https://doi.org/10.3934/mbe.2022458.
Iranian Journal of Mathematical Chemistry
Volume 17, Issue 2
In Progress
June 2026
Pages 179-199

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