Computing the irregularity strength of planar graphs (Q1634487)

Summary: The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total \(k\) labeling of three planar graphs. If such labeling exists for minimum value of a positive integer \(k\), then this labeling is called totally irregular total \(k\) labeling and \(k\) is known as the total irregularity strength of a graph \(G\). More preciously, we determine the exact value of the total irregularity strength of three planar graphs.