Irregularity strength of regular graphs of large degree (Q685644)

It is proved that if \(G\) is an \(n-3\) or \(n-4\) regular graph of order \(n\) (except for \(G=K_{3,3})\), then the irregularity strength of \(G\) is 3, where the irregularity strength of a graph \(G\) is the smallest possible value of \(k\) for which we can assign positive integers less than or equal to \(k\) such that the sums at each vertex are distinct. It is also conjectured that if \(r \geq n/2\), then any \(r\)-regular graph has irregularity strength 3 except for complete bipartite graphs \(K_{t,t}\) with \(t\) odd.