AbstractA totally irregular total k-labeling λ: V ∪ E → {1, 2, · · ·, k} of a graph G is a total labeling such that G has a total edge irregular labeling and a total vertex irregular labeling at the same time. The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we investigate some graphs whose total irregularity strength equals to the lower bound