Explicit Formulas and Bounds on General Randic Index for Complex Graph Models

Abstract

In chemical graph theory, a topological index is a numeric value extracted from the graph ical model of the molecule that provides insight into the structural, physical, bio-active, and chemical properties of the corresponding chemical compound. Randi´c index is very influential, well investigated, and considered to be the prototype of degree-based indices. General Randi´c index Rγ(Γ) is defined as the sum over all edges of the molecular graph Γ with weights dΓ(x)×dΓ(y) γ when γ is a positive integer. Graph operations play a phenomenal role in obtaining new and complex graphs, either of general or of chemical in terest. It is pertinent to explore various graph operations to establish a relationship with the topological indices of the base graphs. In this article, we intend to derive some explicit ex pressions and bounds on the general Randi´c index when γ ∈ Z+ for various complex graph operations like the cartesian product, tensor product, lexicographic product, strong prod uct, co-normal product, corona product, splices, links, and Haj´ os construction of graphs. Besides, we compute the general Randi´c index by applying the formulas obtained for few small cases to check the validity and reliability of our results.