Neighborhood-prime labeling of snake graphs

Abstract

We study neighborhood-prime labeling in the context of snake graphs of the types $C_k^m$ and $C_{k,q}^m$. In particular, we prove that the snake graphs of the type  $C_k^m$ are neighborhood-prime if and only if either $k \not\equiv 2\pmod 4$ or $m\not\equiv 1\pmod 4$. Further, we also show that $C_{k,2}^m$ and $C_{k,3}^m$ are neighborhood-prime for all $m \ge 2$.