On Prime Labeling of Snake Graphs

One of the most active research areas in Graph theory is Graph labeling which is an assignment of integers to
the vertices or edges, or both, subject to certain conditions. This concept was introduced by Alexander Rosa
in 1967 [1]. Since then, it has gathered tremendous pace with a wealth of papers written on various types of
labeling of graphs such as graceful, magic, and neighborhood, to name a few [2], [3]. In the present study, we
focus specifically on prime labeling [4] on snake graphs [5]. In recent years, there has been a growing interest in
the study of prime labeling of graphs [6], [7], which involves assigning distinct prime numbers to the vertices of a
graph in such a way that the labels of any two adjacent vertices are relatively prime. One specific type of graph
that has been the focus of such investigations is the snake graph, which is formed by fusing together multiple
cycles with a shared vertex. In our research, we build upon the work of Bigham et al. [8] to investigate prime
labeling of snake graphs with varying k and q values, where k and q represent the cycle length and minimum
path length, respectively. Specifically, our study is carried out to answer a couple of questions (out of five) raised
in [8].