PRIME LABELING OF AMALGAMATION OF FLOWER GRAPHS

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Abstract
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 with a vertex-set and an edge-set . The order of graph , denoted by , is the number of vertices on . The prime labeling is a bijective function , such that the labels of any two adjacent vertices in G are relatively prime or , for every two adjacent vertices and in . 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 by connecting its pendant vertices (the vertices have degree one) to the central vertex of , such a flower graph is denoted as 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 is a graph formed by taking all by taking all the and identifying their fixed vertices . If , then we write with . In previous research, it has been shown that the flower graphs , for are prime graphs. Continuing the research, we prove that two classes of amalgamation of flower graphs are prime graphs.

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