Relations between Ordinary and Multiplicative Degree-Based Topological Indices

Let G be a simple connected graph with n vertices and m edges, and sequence of vertex degrees d(1) >= d(2) >= center dot center dot center dot >= d(n) > 0. If vertices i and j are adjacent, we write i similar to j. Denote by Pi(1), Pi(1)*, Q(alpha) and H-alpha the multiplicative Zagreb index, multiplicative sum Zagreb index, general first Zagreb index, and general sum-connectivity index, respectively. These indices are defined as Pi(1) = Pi(n)(i=1) d(i)(2), Pi(1)* = Pi(i similar to j)(d(i) + d(j)), Q(alpha) = Sigma(n)(alpha)(i=1) d(i)(alpha) and H-alpha = Sigma(i similar to j)(d(i) + d(j))(alpha). We establish upper and lower bounds for the differences H-alpha - m(Pi(1)*)(m) and Q alpha- n (Pi(1))(alpha/2n). In this way we generalize a number of results that were earlier reported in the literature.