Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let G be a connected graph of order n with m edges and diameter d . The Wiener index W ( G ) and the multiplicative Wiener index π ( G ) of the graph G are equal, respectively, to the sum and product of the distances beten all pairs of vertices of G .  obtain a lor bound for the difference π ( G ) - W ( G ) of bipartite graphs. From it,  prove that π ( G ) W ( G ) holds for all connected bipartite graphs, except P 2 , P 3 , and C 4 .  also establish sufficient conditions for the validity of π ( G ) W ( G ) in the general case. Finally, a relation beten W ( G ) , π ( G ) , n , m , and d is obtained.
['Kinkar Chandra Das', 'Ivan Gutman']
I am writing a research paper on a idea On Wiener and multiplicative Wiener indices of graphs
[{"from": "human", "value": "I am writing a research paper on a idea On Wiener and multiplicative Wiener indices of graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let G be a connected graph of order n with m edges and diameter d . The Wiener index W ( G ) and the multiplicative Wiener index \u03c0 ( G ) of the graph G are equal, respectively, to the sum and product of the distances beten all pairs of vertices of G .  obtain a lor bound for the difference \u03c0 ( G ) - W ( G ) of bipartite graphs. From it,  prove that \u03c0 ( G ) W ( G ) holds for all connected bipartite graphs, except P 2 , P 3 , and C 4 .  also establish sufficient conditions for the validity of \u03c0 ( G ) W ( G ) in the general case. Finally, a relation beten W ( G ) , \u03c0 ( G ) , n , m , and d is obtained."}]