A Unified Approach to Total Vertex Irregularity Strength

Abstract

We develop a unified framework for computing the total vertex irregularity strength (tvs) of diverse graph classes, significantly extending our prior work in Barra et al. This comprehensive approach generalizes and enhances earlier methods, offering a robust technique applicable to a wide range of graph structures. A notable achievement is resolving an open problem by determining the tvs for simple 2-regular graphs, confirming the conjecture by Ahmad et al. Furthermore, our framework provides unified proofs for the tvs of cycles, paths, prisms, wheels, helm graphs, and friendship graphs. Importantly, the versatility of this method suggests its potential utility in computing tvs for additional graph classes, broadening its impact in graph theory and computational applications.