Gracefully Labeling Prisms

Abstract

We provide graceful labelings for prisms $C_{2m}\times P_n$, with even cycles, for all $n\ge 2$, and prisms $C_{2m+1}\times P_n$, with odd cycles when $3\le mn\le 12$. Further, we verify that the windmill graph $K_4^{(m)}$ is graceful for $r\le 22$, and that the square of a path $P_n$ is graceful for $n\le 32$.