On bounds for harmonic topological index

Abstract

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+dj. Lower and upper bounds for invariant H(G) are obtained.