THE IRREGULARITY STRENGTH OF TP3

Let (a1,...,a(t), b1,...,b(t)) be sequence of distinct positive integers such that a(i) + b(i) are distinct for i = 1,...,t, and different from a(j) and b(j), 1 less-than-or-equal-to j less-than-or-equal-to t. Denote by s(t) the minimum of the largest element of these sequences for fixed t. In this note we prove s(t) greater-than-or-equal-to inverted right perpendicular (15t - 1)/7 inverted right perpendicular + 1 for every t. As a corollary we obtain that the irregularity strength of the graph G = tP3, the disjoint union of t paths of length 3, is about 5n/7, where n = 3t is the order of G.