Comment on Complete solution to a conjecture on Randi? index
In this paper we will show that the proof of Theorem 2.1 from Complete solution to a conjecture on Randi? index, by Xueliang Li, Bolian Liu and Jianxi Liu, European Journal of Operational Research 200, Issue 1, (2010), 913, is not correct. They tried to prove the conjecture given by M. Aouchiche, P. Hansen in On a conjecture about the Randi? index (Discrete Mathematics, 307 (2), 2007, 262265), but they failed in it. The mathematical model given by them is a problem of quadratic programming which they tried to solve by wrong use of linear programming. This error invalidates all further work.
conjecture on randi? index linear programming graph theory quadratic programming model errors in proof