Desi Rahmadani, Ardi Aldiansyah, Dina Pratiwi, Mahmuddin Yunus, Vita Kusumasari
Graph labeling is the assigning of labels represented by integers or symbols to graph elements, edges and/or vertices (or both) of a graph. Consider a simple graph G with a vertex-set V(G) and an edge-set E(G). The order of graph G, denoted by |V (G)|, is the number of vertices on G. The prime labeling is a bijective function f:V(G) →{1, 2,..., | V(G)|}, such that the labels of any two adjacent vertices in G are relatively prime or gcd(f(u), f(v)) = 1, for every two adjacent vertices u and v in G. If a graph can be labeled with prime labeling, then the graph can be said to be a prime graph. A flower graph is a graph formed by helm graph Hnby connecting its pendant vertices (the vertices have degree one) to the central vertex of Hnsuch a flower graph is denoted as Fl(n). In this research, we employ constructive and analytical methods to investigate prime labelings on specific graph classes. Definitions, lemmas, and theorems are developed as the main results in this research. The amalgamation Amal(Gi, v0i) is a graph formed by taking all by taking all the Gl's and identifying their fixed vertices v0iIf Gi= Gj= G, then we write Amal(Giv0i) with Amal(G)mIn previous research, it has been shown that the flower graphs Fl(n), for n ≥ 3 are prime graphs. Continuing the research, we prove that two classes of amalgamation of flower graphs Amal(Fl (n)m) are prime graphs. © 2025, The Author(s).
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Jln. Semarang No. 5, Malang, 65145, Indonesia
