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Title: Degree Based Topological Invariants of Operations on Graphs
Authors: Ali, Usman
Keywords: Physical Sciences
Issue Date: 2021
Publisher: University of Management & Technology, Lahore
Abstract: Let H = (V(H),E(H)) be a graph with vertex set V(H) and edge set E(H) ⊆ V(H)×V(H). A topological invariant (TI) is a function that associates a numeric value to the underlying graph. TIs are used to predict the physical and chemical properties of the graphs. These are also used in the study of quantitative structures ac tivity relationships (QSAR) and quantitative structures property relationships (QSPR). Gutman and Trinajstic´ (1972) defined the first degree as well as second degree (connection number) based TIs to calculate the total π-electrone energy of molecules. In the study of hydrocarbons, they also used connection number (number of vertices at distance two) based TI. Recently, connection number based Zagreb indices such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index are widely studied. As per the data provided by International Academy of Mathematical Chemistry, comparatively to the classical Zagreb indices, the chemical capability of the Zagreb connection indices (ZCIs) provides the better absolute values of the correlation coefficients for the thirteen physicochemical properties of octane iso mers such as entropy, acentric factor, density, total surface area, molar volume, boiling point, heat capacity at temperature, heat capacity at pressure, enthalpy of vaporization, standard enthalpy of vaporization, enthalpy of formation, standard enthalpy of formation, and octanol water partition. In this thesis, we compute the general results in the form of exact formulae and upper bounds for the Zagreb connection indices/coindices of the resultant graphs which are obtained by applying operations of Cartesian, lexicographic, tensor, strong, corona, disjunction and symmetric difference. To illustrate the ob tained results, connection based Zagreb indices are also computed for their chemical structures such as linear polyomino chains, carbon nanotubes, fence, closed fence, alkanes and cycloalkanes. Moreover, the connec tion based Zagreb indices and their modified version as modified second ZCI (ZC∗ 2 ) and modified third ZCI (ZC∗ 3 ) are also studied for the subdivision-related operations on graphs. Mainly, a comparison among the old/new ZIs of the subdivision-related operations for the particular classes of alkanes is performed. Finally, we conclude that ZC∗3 -descriptor has more variability than the other ZIs and it may be more considerable for further investigations of several chemical compounds.
Gov't Doc #: 24884
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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