Odd Prime Labeling of Snake Graphs

Abstract

Graph theory is one of the branches of mathematics which is concerned with the networks of points connected by lines. One of the most important research areas in graph theory is graph labeling, which dates back to the 1960s. Graph labeling is assigning integers to the vertices, edges, or both depending on conditions. Labeled graphs are helpful in mathematical models for a wide range of applications such as in coding theory, circuit theory, computer networks, and in cryptography as well. There are various types of graph labeling techniques in graph theory such as radio labeling, graceful labeling, prime labeling, antimagic labeling, and lucky labeling, etc. In this research, we use one of the variations of prime labeling called odd prime labeling of snake graphs. Recent works on odd prime labeling investigate about families of snake graphs, complete graphs, etc and there they discuss about one odd integer sequence only. In this research, we introduce odd prime labeling method for snake graphs for any odd integer sequence and we give a proof for it as well.