A unified approach to total irregular labeling

TL;DR

This paper introduces a unified method to compute the total vertex irregularity strength of various graph classes, simplifying proofs and solving an open problem for 2-regular graphs.

Contribution

It provides a unified framework for calculating tvs across multiple graph types and resolves the tvs for simple 2-regular graphs, advancing graph labeling theory.

Findings

Unified proofs for tvs of cycles, paths, prisms, wheels, complete graphs, helm graphs, friendship graphs, and $K_{n,n}$.

Determined the tvs for simple 2-regular graphs.

Simplified existing calculations and addressed an open problem.

Abstract

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.