Extremal and Computational Invariants of Different Families of Graphs

Abstract

Topological invariants are the significant invariants which are used to study the physico- chemical and thermodynamic characteristics of chemical compound.In this dissertation firstly, we compute the greatest edge Mostar invariant for cacti graph with fixed number of cycles and n vertices. We calculate the sharp upper bound of the edge Mostar invariant for cacti graph. Moreover, we determine the different versions of weighted Mostar invariants for the molecular graphs of three types of dendrimers known as phthalocyanines, triazine and nanostar dendrimers as their cores by the use of the cut method and the numerical way.Secondly, we calculate the M-polynomial, forgotten polynomial, sigma polynomial , som- bor polynomial and different topological invariants of critical importance, referred as first, second, modified and augmented Zagreb, inverse and general Randi´c, harmonic, symmet- ric division, forgotten and inverse invariants of chemical structures namely metal-organic networks (T M TCNB) , cuboctahedral bi-metallic (MOPs) and Trans-Pd-(NH