Maximum Detour–Harary Index for Some Graph Classes

The definition of a Detour⁻Harary index is ω H ( G ) = 1 2 ∑ u , v ∈ V ( G ) 1 l ( u , v | G ) , where G is a simple and connected graph, and l ( u , v | G ) is equal to the length of the longest path between vertices u and v. In this paper, we obtained the maximum Detour⁻Harary index about unicyclic graphs, bicyclic graphs, and cacti, respectively.