The Redefined First, Second and Third Zagreb Indices of Titania Nanotubes TiO2[m,n]

Wei Gao1, *, Mohammad R. Farahani2, Muhammad K. Jamil3, Muhammad K. Siddiqui4
1 School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China
2 Department of Applied Mathematics, Iran University of Science and Technology (IUST) Narmak, Tehran, 16844, Iran
3 Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS) Riphah International University, 14 Ali Road Lahore, Pakistan
4 Department of Mathematics, Comsats Institute of Information Technology, Sahiwal, Pakistan

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© Gao et al.; Licensee Bentham Open

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (, which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this author at the School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China; Tel/Fax: +0871-87646356; E-mail:


The first and the second Zagreb indices are two of the most thoroughly studied and oldest topological indices. Recently in 2013, Ranjini et al. re-defined the Zagreb indices, i.e., the redefined first, second and third Zagreb indices of a graph G are defined as , and , respectively. In this research paper, we compute the redefined Zagreb indices of the Titania Nanotubes TiO2[m, n].

Keywords: Carbon nanotube, Degree of vertex, Molecular graphs, Nano structures, Redefined zagreb indices, Titania nanotubes, Topological indices, Zagreb indices.