EXPLORING RAINBOW COLORING AND CONNECTIVITY ANALYSIS IN HYBRID GRAPH STRUCTURES
Resumo
The study of connectivity in complex networks is a vital area within graph theory and network science. One notable concept that enhances secure and reliable communication is rainbow coloring, here, the edges are colored to ensure that between any two vertices, one can find a path where each edge has a different color. To achieve this condition, the minimum quantity of colors needed is defined as the rainbow connection number.This measure reflects the strength and fault tolerance of network structures and has practical relevance in areas such as secure data transmission and efficient routing protocols.
The research focuses on understanding the role of structural characteristics of graphs on their rainbow connectivity. We provide new insights and results regarding hybrid graph structures like Tribun graph Tn, Chain graph is a point shackle K4Pn, Diamond ladder graph Dln. The results contribute to a deeper understanding of rainbow connection in graph models and contribute to the development of resilient and well-structured communication networks.
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