I am supposed to decide, if the statement is true or false and use arguments for my answer.
In every weighted n-vertices graphs:
with no negative weighted edges,
in which every weighted edge appears constant number of times(e.g. 1,2,3.., but not n number of times), but graphs, in which every edge has the same value, does not satisfy this condition,
there exists between every two vertices at most 4*n^3.
I tried to draw some graphs and I conclude that all of them satisfy my conditions. But I do not have general explanation.
So is that true? If not, can you say me some counter example?