The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures
Mohammed Alsharafi *
Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul, Turkey.
Yusuf Zeren
Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul, Turkey.
Abdu Alameri
Department of Biomedical Engineering, Faculty of Engineering, University of Science and Technology, Yemen.
*Author to whom correspondence should be addressed.
Abstract
In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.
Keywords: Zagreb index, Hyper-Zagreb index, Y-index, Second Hyper-Zagreb index, Forgotten index, graph operation, Titania Nanotubes, V-Phenylenic Nanotube V PHX[q p], V-Phenylenic Nanotorus V PHY [m; n], complement graph