k - Odd Prime Labeling of m×n Grid Graphs

Graph labeling can be mentioned as one of the most prominent research areas in graph theory and the history of graph labeling can be traced back to the 1960s as well. There is a quite number of graph labeling techniques such as graceful labeling, radio labeling, antimagic labeling, prime labeling, and lucky labeling. There are various subtypes of prime labeling including odd prime labeling, k- prime labeling, neighborhood prime labeling, and coprime labeling. In this study, we explore one of the prime labeling varieties called odd prime labeling. There is a well-known conjecture related to this area that all the prime graphs are odd prime graphs. There is a vast number of publications regarding prime labeling and odd prime labeling for different classes of graphs. Recent works on odd prime labeling investigate different types of snake graphs, complete graphs, triangular-type snake graphs, different types of ladder graphs, families of cycle-related and path-related graphs, etc. In this research work, we introduce the concept of k- odd prime labeling and obtain several k- odd prime graphs such as m×n grid graph and variations of it