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 d1 ? d2 ?...? dn > 0. If vertices i and j are adjacent, we write i ~ j. Denote by ?1, ?*1, Q? and H? the multiplicative Zagreb index, multiplicative sum Zagreb index, general first Zagreb index, and general sumconnectivity index, respectively. These indices are defined as ?1 = ?ni=1 d2i, ?*1 = ?i~j(di+dj), Q? = ?n,i=1 d?i and H? = ?i~j(di+dj)?. We establish upper and lower bounds for the differences H?-m (?1*)?/m and Q?-n(?1)?/2n . In this way we generalize a number of results that were earlier reported in the literature.