Document Type : Original Article
Authors
1 Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
2 Divisionof Science and Technology, University of Education, Lahore, 54000, Pakistan
3 Department of Applied Mathematics of Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran
Abstract
Abstract: Let G be the connected graph with vertex set V(G) and edge set E(G).The first and second K Banhatti indices of G are defined as B1(G)=Σue[dG (u) +dG (e)] and B2(G)=Σue[dG (u) +dG (e)] where ue means that the vertex u and edge e are incident in G.The first and second K hyper Banhatti indices of G are defined as HB1(G) = Σue[dg(u) + dG (e)]2 and HB2(G) = Σue[dg(u) dG (e)]2 respectively . In this paper, we compute the first and second K Banhatti indices of toroidal polyhex network. In addition, the first and second K hyper Banhatti indices of toroidal polyhex networks are determined.
Keywords: Topological index, Banhatti index, Network.
Graphical Abstract
Keywords
Main Subjects
- West D B(1996) An Introduction to Graph Theory. Prentice-Hall.
- Rucker G, Rucker C (1999) J. Chem. Inf. Comput. Sci. 39, 788–802.
- Klavžar S, Gutman I (1996). J. Chem. Inf. Comput. Sci. 36, 1001–1003.
- Sardar MS, Zafar S, Farahani MR (2017) Open J. Math. Sci., 1(1), (2017), 44 – 51.
- Rehman HM, Sardar R, Raza A (2017) Open J. Math. Sci., 1(1), (2017), 62 - 71.
- Kulli VR, Chaluvaraju B, Boregowda HS (2017) Journal of Ultra Chemistry, 13(4), 81-87.
- Deza M, Fowler PW, Rassat A, Rogers KM (2000) J. Chem. Inf. Comput. Sci, 40, 550–558.
- Kirby EC, Pollak P (1998) J. Chem. Inf. Comput. Sci, 38, 1256–1256.
- Beuerle F, Herrmann C, Whalley AC, Valente C, Gamburd A, Ratner MA, Stoddart JF (2011) Chem. Eur. J, 17, 3868-3875.
- Ye D, Qi Z, Zhang H (2009) SIAM J. Discret. Math. 23, 1023–1044.
- Kang MH (2011) Discret. Math. 311, 2384–2395.
- Baca M, Horvathova J, Mokrisova M, Suhanyiova A (2015) Appl. Math. Comput. 251, 154–161.
- Mehranian Z, Ashrafi AR (2016) Springer International Publishing: Cham, Switzerland, 281–301.
- Ernesto E, Matamala AR (2008) J. Math. Chem. 43, 508–517.
- Yang H, Sajjad W, Baig AQ, Farahani MR (2017) International Journal of Advanced Biotechnology and Research. 8(2), 1582-1589.
- Huo Y, Liu JB, Baig AQ, Sajjad W, Farahani MR (2017). Journal of Computational and Theoretical Nanoscience. 14(4), 1832–1836.
- Dhavaseelan R, Baig AQ, Sajjad W, Farahani MR (2017) Journal of Informatics and Mathematical Sciences. 9(1), 201–215.
- Rezaei M, Baig AQ, Sajjad W, Farahani MR (2016). International Journal of Pure and Applied Mathematics. 111(3), 467-477.
- Farahani MR, Baig AQ, Sajjad W, Ramane HS (2018) International Journal of Advances in Mathematics. 1, 101-108.
- Gao W, Shi L, Farahani MR (2017) Journal of Discrete Mathematical Sciences and Cryptography, 20(2), 553-563.
- Farahani MR (2012) Acta Chim. Slov. 59, 779–783.
- Farahani MR (2012) Sci-Afric Journal of Scientific Issues, Research and Essays. 2(12), 567-570, 2014.
- Gao Y., Farahani M.R., Nazeer W (2018) Chemical Methodologies. 3, 39-45.