Summary: A vertex irregular total \(k\)-labeling of a graph \(G\) with vertex set \(V\) and edge set \(E\) is an assignment of positive integer labels \(\{1, 2, \dots, k\}\) to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of \(G\), denoted by \(\text{tvs}(G)\) is the minimum value of the largest label \(k\) over all such irregular assignment. In this paper, we consider the total vertex irregularity strengths of disjoint union of \(s\) isomorphic sun graphs, \(\text{tvs}(sM_n)\), disjoint union of \(s\) consecutive nonisomorphic sun graphs, \(\text{tvs}(\bigcup^s_{i=1} M_{i+2})\), and disjoint union of any two nonisomorphic sun graphs \(\text{tvs}(M_k \cup M_n)\).