On Prime Labeling of Snake Graphs
P. G. R. S. Ranasinghe, L. R. M. K. R. Jayathilaka · Journal of Advances in Mathematics and Computer Science · 2023
A snake graph C m (k,q) is the fusion of m number of k-cycles, C k , such that, for 2 ≤ i ≤ m, a shared vertex called the vertebrae, denoted by vi, results from the fusion where a minimal path of length q joins v (i-1) and vi.In the present study, we focus on a few questions on prime labeling of snake graphs as stated in Bigham et al. when each cycle of snake does not have the same k or q values and the minimum m for which C m (2,q) when k is odd and greater than 2. To find the prime labeling for snake graphs for different k values, we label the graph using the modified snake labeling when q = 2.To obtain a possible snake labeling, we consider the modified snake labeling for q = 2, by considering all the possibilities.To find the maximum value of m, we implement a Python program to obtain the smallest prime factor of k -2 for all odd numbers up to any given number.We obtain a general pattern for the maximum m value considering the above results.