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Open AccessArticle

Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks

1
Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, Pakistan
2
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(8), 1320; https://doi.org/10.3390/sym12081320
Received: 22 July 2020 / Revised: 3 August 2020 / Accepted: 5 August 2020 / Published: 7 August 2020
(This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices)
Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks. View Full-Text
Keywords: connection number; Zagreb indices; coindices; product of networks connection number; Zagreb indices; coindices; product of networks
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Ali, U.; Javaid, M.; Alanazi, A.M. Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks. Symmetry 2020, 12, 1320.

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