Naila Cahaya Putri, Desi Rahmadani, Andrea Semanicova-Fenovcikova
A graph G(p,q) with p = |K(G)| and q — \E(G)\ is said to be odd harmonious if there exists an injective function/: V(G) -> {0,1,2,... ,2q — 1} such that the induced mapping f*:E(G) -> {1, 3, 5, ...,2q - 1} with/* (uv) — f(u) + f(v) is bijective, / is said to be an odd harmonious labeling of the graph G. The stemmed subdivided shell graph is a graph constructed from the subdivided shell graph SSn and the path Pm by connecting the apex of the subdivided shell graph SSn to one of the pendant points of the path Pm. The stemmed subdivided shell graph is denoted by SSSmn. Amalgamation of stemmed subdivided shell graph SSS2n, denoted by Amal(SSS2n)r is a graph constructed by copying the graph SSS2iTl for r copies and identifying the pendant points of r copies of the graph SSS2n. The determination of odd harmonious labeling for the graph SSSmn and graph Amal(SSS2n)r is still an open issue. In this paper it will be shown that the graph SSSmn for every m,n > 2 and the graph Amal(SSS2n)r for every 2 < r < n are odd harmonious. The method used to show that the graph is odd harmonious is by using the following steps: study the literature about odd harmonious labeling, define the graph to be studied, determine the odd harmonious labeling on the graph, formulate the odd harmonious labeling pattern on the graph in general, create an odd harmonious labeling theorem on the graph, prove the theorem that has been made mathematically, and make a conclusion. © 2025 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Faculty of Mathematics and Natural Sciences Universitas Negeri Malang, Jl. Semarang 5, Malang, 65145, Indonesia; Department ofApplied Mathematics and Informatics, Technical University, Kosice, 042 00, Slovakia
