Relations between ordinary and multiplicative degree-based topological indices

Abstract

Let G be a simple connected graph with n vertices and m edges, and sequence of vertex degrees d 1 ≥ d 2 ≥ · · · ≥ d n > 0. If vertices i and j are adjacent, we write i ∼ j. Denote by Π 1 , Π ∗1 , Q α and H α the multiplicative index, multiplicative sum Zagreb index, and general sum-connectivity index, respectively. These indices are defined as (Formula Presented). We establish upper and lower bounds for the differences (Formula presented). In this way we generalize a number of results that were earlier reported in the literature.