Maulidatus Soleha, Purwanto, Desi Rahmadani
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/+ : V(G) -> (0, 1, 2, ..., 2q - 1) given by f+(x) = ΣXyεE(G) f(xy) (mod 2q) is injective. A triangular snake net graph (m - 1) Cm/3 is graph obtained from a path u1u2 u3... um+1 by joining every ut and ul+1 to a new vertex vt with 1 < i < m and joining every vt to vi+1 with 1 < i < m - 1. A quadrilateral snake net graph Cm/4, 4 is a graph obtained from vertices U 1, U 2. U 3, ..., u2m+1 by joining every ut and u i + 1 to two vertices vt and v2i-1 with 1 < i < 2m, and joining every v4i_2 and v4l 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(Cm/4, 4) is graph obtained from vertices ult 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 u 3 i to two new vertices v4i-1 and v4i, joining v4i-3 and v4i-1 to a new vertex w2i-1 and joining v 4 i - 2 and V4i to two a new vertex w2i with 1 < i < m. A quadrilateral pleated snake graph C4(m) is a graph obtained from vertices u0, u, and v by joining every u0 and u to new vertices ut and joining every u0 and v to new vertices vt with 1 < t < 2m + 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. © 2022 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Jalan Semarang 5, Malang, 65145, Indonesia