LAUSR

Let G = (V,E), V = {1, 2, . . . ,n}, E = {e1, e2, . . . , em}, be a simple graph with n vertices and m edges. Denote by d1 ≥ d2 ≥ · · · ≥ dn > 0 and d(e1) ≥ d(e2) ≥ · · · ≥ d(em), sequences of vertex and edge degrees, respectively. If i-th and j-th vertices of the graph G are adjacent, it is denoted as i ∼ j. Graph invariant referred to as harmonic index is defined as H(G) = ∑ i∼ j 2 di + d j . Lower and upper bounds for invariant H(G) are obtained.