Hafsah Ayu Wibowo, Desi Rahmadani
Graph labeling is the assignment of values to the vertices or edges of a graph (or both) in such a way that certain conditions are satisfied for every u, v £ V(G). A graph G(p, q) with p vertices and q edges is said to be odd harmonious if there exists an injective function f: V(G) -> {0,1,2, ...,2q — 1} such that the induced function /*:£'(G)-> [1,3,5, ...,2q — 1} defined by f*(uv) — /(it) + f(y) is bijective. The graph resulting from the edge comb product operation on the path graph and the prism graph, denoted by Pn > Y4 2 is a graph formed by taking one copy of Pn and E(Pn) | copies of Y4 2, then attaching the i-th copy of Y4 2 at the edge e to the i-th edge of Pn. Similarly, the graph Pn > Y6 2 is formed by taking one copies of Pn and |E(Pn) | copies of Y6 2, then attaching the i-th copy of Y6 2 at the edge e to the i-th edge of Pn. In this research, prove that the graphs Pn > Y4 2 and Pn > Y6 2 are odd harmonious graphs. © 2025 American Institute of Physics Inc.. All rights reserved.
Department ofMathematics, Faculty ofMathematics and Natural Sciences, Universitas Negeri, Malang, Jl. Semarang 5, Malang, 65145, Indonesia
