Edge odd graceful labeling of some snake net and pleated snake graphs
Maulidatus Soleha, Purwanto Purwanto, Desi Rahmadani · AIP conference proceedings · 2022
An edge odd graceful labeling of graph G with q number of edges 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) = ExyEE(G) f(xy) (mod 2q) is injective. A triangular snake net graph (m - 1)C3m is graph obtained from a path u1 u2 u3 … um + 1 by joining every ui and ui + 1 to a new vertex vi with 1 ≤ i ≤ m and joining every vi to vi+1 with 1 ≤ i ≤ m - 1. A quadrilateral snake net graph C4,4m is a graph obtained from vertices u1, u2, u3, …, u2m + 1 by joining every ui and ui + 1 to two vertices vi and v2i-1with 1 ≤ i ≤ 2m, and joining every v4i - 2 and v4i to a new vertex w2i and joining every v4i - 3 and v4i-1 to a new vertex w2i - 1 with 1 ≤ i ≤ m. An alternate quadrilateral snake net A(C4,4m) is graph obtained from vertices u1, u2, u3, … , u3m by joining every u3i and u3i + 1 with 1 ≤ i ≤ m - 1, and joining u3i - 2 and u3i - 1 to two new vertices v4i-3 and v4i-2, joining u3i-1 and u3i to two new vertices v4i-1 and v4i, joining v4i-3 and v4i-1 to a new vertex w2i-1, and joining v4i-2 and v4i to two a new vertex w2i with 1 ≤ i ≤ m. A quadrilateral pleated snake graph C42 is a graph obtained from vertices u0, u, and v by joining every u0 and u to new vertices ui and joining every u0 and v to new vertices vi with 1 ≤ i ≤ 2 m + 2. In this paper, we study edge odd graceful labeling for the following families of snake graphs such as triangular snake net, quadrilateral snake net, alternate quadrilateral snake net, and quadrilateral pleated snake.