Fibonacci Prime Labelling on the Class of Flower Graphs

Graph labeling is one of the significant topics in graph theory. One of its interesting variants is Fibonacci prime labeling, a special type of labeling that assigns Fibonacci numbers as vertex labels while satisfying certain conditions. A graph labeling is an assignment of labels (elements of some set) to elements of a graph, usually the vertices or the edges (or both) of the graph. Several previous studies have shown that some classes of graphs, such as cycle graphs, fan graphs, and umbrella graphs, satisfy the criteria for Fibonacci prime labeling. Moreover, previous research has proven that flower graphs and double flower graphs admit prime labeling. Motivated by these findings, this study aims to explore whether these two classes of graphs also admit Fibonacci prime labeling. This exploration seeks to identify a potential relationship between prime labeling and Fibonacci prime labeling in these graph classes. This research focuses on graphs with an even number of vertices. The methods used include literature review and mathematical proof. The novelty of this study lies in extending the results of prime labeling to Fibonacci prime labeling for flower and double flower graphs. The results show that both graph classes with an even number of vertices belong to the class of graphs that admit Fibonacci prime labeling.