Multiplicative degree-based topological indices and line graph of hex board graph

Amin, Shahid; Rehman, Muhammad Aziz Ur; Farahani, Mohammad Reza; Cancan, Murat; Aldemir, Mehmet Serif

doi:10.22034/ecc.2020.255142.1093

Document Type : Original Research Article

Authors

¹ Department of Mathematics, University of Management and Technology, Lahore, Pakistan

² Department of Mathematics, Iran University of Science and Technology (IUST) Narmak, 16844, Tehran, Iran

³ Faculty of Education, Van Yuzuncu Yıl University, Zeve Campus, Tuşba, 65080, Van, Turkey

⁴ Faculty of Science, Van Yuzuncu Yıl University, Zeve Campus, Tuşba, 65080, Van, Turkey

https://doi.org/10.22034/ecc.2020.255142.1093

Abstract

Mathematical chemistry is the area of research in mathematics, in which problems of chemistry are solved by utilizing techniques of mathematics. In mathematical chemistry, a number is assigned to molecular graph of compound called topological index (TI) which depends on the topology of compound and helps us in deciding properties of concerned compound. TIs usually depend on the degree of vertices in a graph, distances and spectrum, among which degree depending TIs are studied extensively in recent years and have led to huge applications in theoretical chemistry, drugs formulation and pharmacy. This paper aimed to compute some degree depending TIs of Hex board networks and line graph of hex board networks. The generalized first and second multiplicative Zagreb indices (ZIs), multiplicative version of Atomic bond connectivity index (ABC) and generalized multiplicative Geometric Arithmetic index (GA) of Hex board and the line graph of Hex board networks were computed in this study.

Graphical Abstract

Keywords

Main Subjects

Computational Chemistry

References

[1] D.B. West, Introduction to graph theory (2). Uer Saddle River: Prentice hall. 2001.

[2] D. Bonchev, Chemical graph theory: introduction and fundamentals (1). CRC Press. 1991.

[3] H. Hosoya, M. Miyuki, G. Machiko, Natural Science Report, 1973, 24, 27-34.

[4] E. Deutsch, S. Klavžar, arXiv preprint arXiv: 1407.1592. 2014.

[5] Y.C. Kwun, M. Munir, W. Nazeer, S. Rafique, S.M. Kang, Scientific reports, 2017, 7, 8756-8764.

[6] A. Ali, W. Nazeer, M. Munir, S.M. Kang, Open Chem., 2018, 16, 73-78.

[7] M. Munir, W. Nazeer, S.M. Kang, M.I. Qureshi, A.R. Nizami, Y.C. Kwun, Symmetry, 2017, 9, 17-25

[8] S.M. Kang, W. Nazeer, M.A. Zahid, A.R. Nizami, A. Aslam, M. Munir, Open Physics, 2018, 16, 394-403.

[9] S.M. Kang, W. Nazeer, W. Gao, D. Afzal, S.N. Gillani, Open Chem., 2018, 16, 201-213.

[10] W. Nazeer, A. Farooq, M. Younas, M. Munir, S. Kang, Biomolecules, 2018, 8,92-100.

[11] H.M. Rehman, R. Sardar, A. Raza, Open J. Math. Sci., 2017, 1,62-71.

[12] H. Wiener, J. Am. Chem. Soc., 1947, 69, 17–20.

[13]A.A. Dobrynin, R. Entringer,I. Gutman,Acta Al. Math., 2001, 66, 211–249.

[14]I. Gutman, O.E. Polansky, Springer-Verlag: New York, NY, USA, 1986.

[15] M. Randić, J. Am. Chem. Soc., 1975, 97,6609–6615.

[16] B. Bollobas, P. Erdos, Ars Combin., 1998,50, 225–233.

[17] D. Amic, D. Beslo, B. Lucic, S. Nikolic, N. Trinajstic´, J. Chem. Inf. Comput. Sci., 1998, 38,819–822.

[18] Y. Hu, X. Li, Y. Shi, T. Xu, I. Gutman, MATCH Commun. Math. Comput. Chem., 2005, 54, 425–434.

[19] G. Caporossi, I. Gutman, P. Hansen, L. Pavlovic, Comput. Biol. Chem., 2003, 27,85–90.

[20] X. Li, I. Gutman, Math. Chem. Mono., 1, Kragujevac, 2006.

[21] L.B. Kier, L.H. Hall, Academic Press, New York, 1976.

[22] L.B. Kier, L.H. Hall, Wiley, New York, 1986.

[23] I. Gutman, N. Trinajstić, Chem. Phys. Lett., 1972, 17, 535–538.

[24] M. Eliasi, D. Vukičević, MATCH Commun. Math. Comput. Chem., 2013, 69, 765-773.

[25] I. Gutman, B. Ruscić, N. Trinajstić, C.F. Wilcox Jr, J. Chem. Phys., 1975, 62, 3399-3405.

[26] H. Narumi, M. Katayama, Hokkaido University, 1984, 16, 209-214.

[27] I. Gutman, Bull. Soc. Math. Banja Luka, 2011, 18, 17-23.

[28] R. Todeschini, D. Ballabio, Consonni V., Math. Chem. Mono., 2010, 73-100.

[29] R. Todeschini, V. Consonni, MATCH Commun. Math. Comput. Chem., 2010, 64, 359-372.

[30] S. Wang, B. Wei, Dis. Alied Math., 2015, 180, 168-175.

[31] M. Eliasi, A. Iranmanesh, I. Gutman,MATCH Commun. Math. Comput. Chem., 2012, 68, 217-230.

[32], V.R. Kulli, Int. Res. J. Pure Algebra ISSN: 2248-9037, 6, 2016.

[33] V.R. Kulli, B. Stone, S. Wang, B. Wei, Z. Naturforsch. A,2017, 72, 573-576.

[34] V.R. Kulli,J. Comput. Math. Sci., 2016, 7, 599-605.

[35] W. Gao, M.K. Siddiqui, M. Imran, M.K. Jamil, M.R. Farahani, Saudi Pharm. J., 2016, 24, 258-264.

[36] W. Gao, M.R. Farahani, L. Shi, Acta Medica Medit., 2016, 32,579-585.

[37] W. Gao, W. Wang, M.R. Farahani, J. Chem., 2016, 2016, Article ID 3216327.

[38] Z. Tang, L. Liang, W. Gao, Open J. Math. Sci.,2018, 2,73-83.

[39] M.S. Sardar, S. Zafar, M.R. Farahani, Open J. Math. Sci.,2017, 1, 44–51.

[40] M.S. Sardar, X.F. Pan, W. Gao, M.R. Farahani, Open J. Math. Sci., 2017, 1,126–131

[41] H. Siddiqui, M.R. Farahani, Open J. Math. Anal., 2017, 1, 45-60.

[42] W. Gao, M. Asif, W. Nazeer, Open J. Math. Anal., 2018,2, 10-26.

[43] M.R. Farahani, Acta Chim. Slov., 2012, 59, 779–783.

Eurasian Chemical Communications

Multiplicative degree-based topological indices and line graph of hex board graph

References

References

Volume 2, Issue 11
November 2020
Pages 1137-1145

Multiplicative degree-based topological indices and line graph of hex board graph

References

References

Volume 2, Issue 11November 2020Pages 1137-1145

Volume 2, Issue 11
November 2020
Pages 1137-1145