On bounds for harmonic topological index

Marjan Matejic, Igor Milovanovic, Emina Milovanovic
2018 Filomat  
Let G = (V, E), V = {1, 2, . . . , n}, E = {e 1 , e 2 , . . . , e m }, be a simple graph with n vertices and m edges. Denote by d 1 ≥ d 2 ≥ · · · ≥ d n > 0 and d(e 1 ) ≥ d(e 2 ) ≥ · · · ≥ d(e m ), 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 d i + d j . Lower and upper bounds for invariant H(G) are obtained.
doi:10.2298/fil1801311m fatcat:phfpztexwzc5vd5gdzdydyuj44