Let G(V, E) be a simple graph. For a labeling ∂:V∪E→{1,2,3,..,k} the weight of a vertex x is defined as (Formula Presented) is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y wt(x)≠wt(y). The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G and it is denoted by tvs(G). In this paper we determine the total vertex irregularity strength of 1-fault tolerant hamiltonian graphs CH(n),H(n) and W(m). © 2015, Springer Basel.