Edge odd graceful of alternate snake graphs

Abstract

Let G be a graph with vertex set V(G), edge set E(G), and the number of edges q. An edge odd graceful labeling of G is a bijection f : E(G) → {1,3,5, …,2q − 1} so that induced mapping f + : V(G) → {0,1,2, …,2q − 1} given by f +(x) = ∑ xy∈E(G) f(xy) (mod 2q) is injective. A graph which admits an edge odd graceful labeling is called edge odd graceful. An alternate triangular snake graph is a graph obtained from a path u 1 u 2 u 3 … u 2m by joining every u 2i−1 and u 2i to a new vertex υi , 1 ≤ i ≤ m. An alternate quadrilateral snake graph is a graph obtained from vertices u 1, u 2,u 3,…,u 2m by joining every u 2i−1 and u 2i to two vertices υi and wi ,1 ≤ i ≤ m, and joining every u 2i to u 2i+1 with 1 ≤ i ≤ m − 1. In this paper, we show that alternate triangular snake and alternate quadrilateral snake graphs are edge odd graceful.