Problem

Source: Iran TST1 Day1 P1

Tags: combinatorics, graph theory, Iranian TST



A weighted complete graph with distinct positive wights is given such that in every triangle is degenerate that is wight of an edge is equal to sum of two other. Prove that one can assign values to the vertexes of this graph such that the wight of each edge is the difference between two assigned values of the endpoints. Proposed by Morteza Saghafian