Zagreb Connection Indices of Molecular Graphs Based on Operations. (30th March 2020)

• Record Type: Journal Article
• Authors: Cao, Jinde; Ali, Usman; Javaid, Muhammad; Huang, Chuangxia
• Other Names: Wang Qingling Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-03-30
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/7385682
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. The Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic Mol . Inform . 37 2018, 1 − 7 restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu ). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included.