Odd-even graceful labeling of planar grid and prism graphs

Abstract

A graph G with p vertices and q edges is said to be odd-even graceful graph, if there exist an injective function f : V(G) → {1, 3, 5, … , 2q + 1} such that induced function f * : E(G) → {2, 4, 6, … , 2q} defined by f *(uv) =| f (u) − f (v)| for every uv ∈ E(G) is a bijection. In this paper we proved that the planar grid and the prism admit odd-even graceful labeling.

Subject Classification:

• 05C78

Keywords:

• Labeling
• Graceful labeling
• Odd-even graceful labeling
• Cartesian product graph