Abstract
The two key parameters in this study of graph theory are the rainbow connected number and strongly rainbow connected numbers. The purpose of this study is to identify the strongly rainbow connected numbers of the inverse graphs corresponding to the modular groups under various operations, and to evaluate and explain the characteristics of these numbers in various contexts.The objective of this Study is to apply these concepts and results in the field of Networking and Coding. An edge colored graph G is called rainbow-connected if a path whose edges have different colors that connects any two vertices. The minimum k for which there exist a rainbow k−coloring of G is called the rainbow connection number of G, denoted by rc(G), the adjacent edges may be allowed to color with the same color. The graph G is strongly rainbow connected if there exists a rainbow u-v geodesic for every pair of vertices u and v in G.
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