Forgotten Coindex for the Derived Sum Graphs under Cartesian Product

Abstract

A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H. For D∈S,R,Q,T and the connected graph H, the derived graphs DH are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph (D-sum graph) is obtained by the Cartesian product of the graph H2 with the graph DH1. In this study, we compute forgotten coindex of the D-sum graphs H1+SH2 (S-sum), H1+RH2 (R-sum), H1+QH2 (Q-sum), and H1+TH2 (T-sum) in the form of various indices and coindices of the factor graphs H1 and H2. At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D-sum graphs.