Sombor Symmetric Division Degree Index and Co-index of Graph Operations

Abstract

In the present study, we introduce two new graph invariants called Sombor symmetric division
index and coindex, and discuss their properties with reference to certain graphs. Also, we compute their
values for some of the graph operations such as the Cartesian product, composition, direct product and strong
product of two graphs. Further, we establish bounds on these invariants in terms of other graph parameters
and work on the relation between them. Through a correlative analysis with the π-electron energy of a few
chosen hetero molecules and PAHs, the chemical application of these parameters is examined.