Geodesic
On the Hosoya polynomial of the third type of the chain hex-derived network
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2022), pp. 67-78.

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A topological index plays an important role in characterising various physical properties, biological activities, and chemical reactivities of a molecular graph. The Hosoya polynomial is used to evaluate the distance-based topological indices such as the Wiener index, hyper-Wiener index, Harary index, and Tratch-Stankevitch-Zefirov index. In the present study, we determine a closed form of the Hosoya polynomial for the third type of the chain hex-derived network of dimension $n$ and derive the distance-based topological indices of the network with the help of their direct formulas and alternatively via using the obtained Hosoya polynomial. Finally, we graphically represent the computed distance-based topological indices and the Hosoya polynomial of the underlying network to comprehend their geometrical pattern. This study of the Hosoya polynomial and the corresponding indices can set the basis for more exploration into chain hex-derived networks and their properties.
Keywords: graphical indices; topological index; third type of chain hex-derived network; distance-based topological indices; Hosoya polynomial; graph polynomial. 
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D. Shibsankar; R. Shikha. On the Hosoya polynomial of the third type of the chain hex-derived network. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2022), pp. 67-78. http://geodesic.mathdoc.fr/item/BGUMI_2022_3_a5/

[1] D. B. West, Introduction to graph theory, Prentice Hall, Hoboken, 2001, 588 pp.

[2] A. T. Balaban, Chemical applications of graph theory, Academic Press, London, 1976, 389 pp. | MR

[3] R. Garcia-Domenech, J. Galvez, Julian-Ortiz. de, L. Pogliani, “Some new trends in chemical graph theory”, Chemical Reviews, 108(3) (2008), 1127–1169 | DOI

[4] A. T. Balaban, “Highly discriminating distance-based topological index”, Chemical Physics Letters, 89(5) (1982), 399–404 | DOI | MR

[5] I. Gutman, “Degree-based topological indices”, Croatica Chemica Acta, 86(4) (2013), 351–361 | DOI

[6] K. Pattabiraman, “Degree and distance based topological indices of graphs”, Electronic Notes in Discrete Mathematics, 63 (2017), 145–159 | DOI | MR

[7] P. V. Khadikar, N. V. Deshpande, P. P. Kale, A. Dobrynin, I. Gutman, G. Domotor, “The Szeged index and an analogy with the Wiener index”, Journal of Chemical Information and Computer Sciences, 35(3) (1995), 547–550 | DOI

[8] I. Gutman, “The acyclic polynomial of a graph”, Publications de I’Institut Mathematique, 22(36) (1977), 63–69 | MR

[9] E. J. Farrell, “An introduction to matching polynomials”, Journal of Combinatorial Theory, 27(1) (1979), 75–86 | DOI | MR

[10] Haruo. Hosoya, “On some counting polynomials in chemistry”, Discrete Applied Mathematics, 19(1–3) (1988), 239–257 | DOI | MR

[11] L. H. Kauffman, “A Tutte polynomial for signed graphs”, Discrete Applied Mathematics, 25(1–2) (1989), 105–127 | DOI | MR

[12] Heping. Zhang, Fuji. Zhang, “The Clar covering polynomial of hexagonal systems I”, Discrete Applied Mathematics, 69(1–2) (1996), 147–167 | DOI | MR

[13] I. Gutman, “Some relations between distance-based polynomials of trees”, Bulletin Classe des Sciences Mathématiques et Naturelles, 131(30) (2005), 1–7 | DOI | MR

[14] E. Deutsch, S. Klavžar, “M-polynomial and degree-based topological indices”, Iranian Journal of Mathematical Chemistry, 6(2) (2015), 93–102 | DOI

[15] S. Das, V. Kumar, “Investigation of closed derivation formula for GQ and QG indices of a graph via M-polynomial”, Iranian Journal of Mathematical Chemistry, 13(2) (2022), 129–144 | DOI

[16] I. Gutman, S. Klavzar, M. Petkovsek, Pletersek. Zigert, “On Hosoya polynomials of benzenoid graphs”, MATCH. Communications in Mathematical and in Computer Chemistry, 43 (2001), 49–66 | MR

[17] A. A. Ali, A. M. Ali, “Hosoya polynomials of pentachains”, MATCH. Communications in Mathematical and in Computer Chemistry, 65 (2011), 807–819 | MR

[18] A. Sadeghieh, S. Alikhani, N. Ghanbari, AJM. Khalaf, “Hosoya polynomial of some cactus chains”, Cogent Mathematics, 4(1) (2017), 1305638 | DOI | MR

[19] T. Novak, Poklukar. Rupnik, J. Zerovnik, “The Hosoya polynomial of double weighted graphs”, ARS Mathematica Contemporanea, 15(2) (2018), 441–466 | DOI | MR

[20] Shoujun. Xu, Qinghua. He, Shan. Zhou, Waihong. Chan, “Hosoya polynomials of random benzenoid chains”, Iranian Journal of Mathematical Chemistry, 7(1) (2016), 29–38 | DOI | MR

[21] W. Dejun, H. Ahmad, W. Nazeer, “Hosoya and Harary polynomials of TUC4 nanotube”, Mathematical Methods in the Applied Sciences, 2020, 6487 | DOI | MR

[22] M. Numan, A. Nawaz, A. Aslam, S. I. Butt, “Hosoya polynomial for subdivided caterpillar graphs”, Combinatorial Chemistry and High Throughput Screening, 25(3) (2022), 554–559 | DOI

[23] B. Şahin, A. Şahin, “The Hosoya polynomial of the Schreier graphs of the Grigorchuk group and the Basilica group”, Turkish Journal of Science, 5(3) (2020), 262–267

[24] K. G. Mirajkar, B. Pooja, “On the Hosoya polynomial and Wiener index of jump graph”, Jordan Journal of Mathematics and Statistics, 13(1) (2020), 37–59 | MR

[25] H. Wiener, “Structural determination of paraffin boiling points”, Journal of the American Chemical Society, 69(1) (1947), 17–20 | DOI

[26] M. Randic, “Novel molecular descriptor for structure-property studies”, Chemical Physics Letters, 211(4–5) (1993), 478–483 | DOI

[27] S. S. Tratch, M. I. Stankevitch, N. S. Zefirov, “Combinatorial models and algorithms in chemistry. The expanded Wiener number – a novel topological index”, Journal of Computational Chemistry, 11(8) (1990), 899–908 | DOI | MR

[28] D. Plavsic, S. Nikolic, N. Trinajstic, Z. Mihalic, “On the Harary index for the characterization of chemical graphs”, Journal of Mathematical Chemistry, 12(1) (1993), 235–250 | DOI | MR

[29] F. M. Bruckler, T. Doslic, A. Graovac, I. Gutman, “On a class of distance-based molecular structure descriptors”, Chemical Physics Letters, 503(4) (2011), 336–338 | DOI | MR

[30] Nocetti. Garcia, I. Stojmenovic, Jingyuan. Zhang, “Addressing and routing in hexagonal networks with applications for tracking mobile users and connection rerouting in cellular networks”, IEEE Transactions on Parallel and Distributed Systems, 13(9) (2002), 963–971 | DOI

[31] P. Manuel, R. Bharati, I. Rajasingh, M. M. Chris, “On minimum metric dimension of honeycomb networks”, Journal of Discrete Algorithms, 6(1) (2008), 20–27 | DOI | MR

[32] F. S. Raj, A. George, “On the metric dimension of HDN3 and PHDN3”, Institute of Electrical and Electronics Engineers. 2017 IEEE International conference on power, control, signals and instrumentation engineering (Chennai, India), Curran Associates, Piscataway, 2018, 1333–1336 | DOI

[33] S. Hayat, M. Imran, “Computation of topological indices of certain networks”, Applied Mathematics and Computation, 240(23) (2014), 213–228 | DOI | MR

[34] S. Das, S. Rai, “M-polynomial and related degree-based topological indices of the third type of chain hex-derived network”, Malaya Journal of Matematik, 8(4) (2020), 1842–1850 | DOI | MR

[35] Changcheng. Wei, H. Ali, M. A. Binyamin, M. N. Naeem, Jiabao. Liu, “Computing degree based topological properties of third type of hex-derived networks”, Mathematics, 7(4) (2019), 368 | DOI

[36] S. Rai, S. Das, “M-polynomial and degree-based topological indices of subdivided chain hex-derived network of type 3”, Advanced network technologies and intelligent computing. 1st International conference (Varanasi, India), Springer, Cham, 2022, 410–424 | MR