A unified approach to total irregular labeling

We present a unified approach to compute the total vertex irregularity strength (tvs) of various graphs, employing a novel technique recently proposed by Barra et al. For graphs such as cycles, paths, prisms, wheels, complete graphs, helm graphs, friendship graphs, and $K_{n,n}$ , we offer simplified and unified proofs of their previously established tvs values. Furthermore, we resolve an open problem by determining the tvs for simple 2-regular graphs.