Regina Ayu Rahmawati, Purwanto
Let G be a finite graph having a vertex set V(G), an edge set E(G), and |E(G)| = q. An odd harmonious labeling of G is an injection f: V(G) → {0, 1, 2, …, 2q − 1} such that the induced mapping f∗: E(G) → {1, 3, 5, …, 2q − 1}, where f∗(uv) = f(u) + f(v), is a bijection. If a graph can be labeled by an odd harmonious labeling, then the graph is said to be odd harmonious. A hedge graph Hn is a graph formed from series of n copies of 4 −cycle, ci = xi−1vi1xivi2xi−1, i = 1, 2, …, n, and 2n vertices wij, j = 1, 2, by joining each vij to wij. A graph K′(2, nc4) is a graph formed from n copies of 4 −cycle, ci = vi1ui1vi2ui2vi1, i = 1, 2, …, n, two vertices u0j, j = 0, 1, and 2n vertices wij, by joining all vertices uij to u0j and each vertex vij to xij. In this paper we show that hedge graph Hn and graph K′(2, nc4) are odd-harmonious. © 2024 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Universitas Negeri Malang, Jalan Semarang 5, Malang, 65145, Indonesia
