Abstract: The m-weighting w of G is a mapping from E(G) to ｛1,2,…,m｝. The image w(e) of each edge e of G is called the weight of e. An mweighting of G is called an m-irregular assignment if, for any two distinct vertices u and v, the sum of the weights of the edges incident with u is different from the sum of the weights of the edges incident with v. The minimum integer m such that G has an mirregular assignment is called the irregularity strength of G. Based on the conception, it is investigated the irregularity strengths of the vertex-disjoint union of t paths with order n(n≡2(mod 4) and n≡3 (mod 4)).

Key words: edge-weighted, irregularity strength, weighted degree, irregular assignments