Minimal Harary index of unicyclic graphs with diameter at most 4

Abstract The Harary index of a graph G is defined as H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 d G ( u , v ) , where dG(u, v) is the distance between the vertices u and v. In this paper, we respectively determine the minimal Harary index among all unicyclic graphs with diameter 3 and all unicyclic graphs with diameter 4.