A Novel Pyramid Graph Construction with the Formulation of Several Graph Theory Applications

Abstract

In this article, we introduced a new graph, let C be the pyramid graph with vertex set V(C) and edge set E(C). Pyramid graphs are a powerful tool for data visualization. By combining multiple cycles into a single graph, they provide a clear and concise representation of complex data sets, analyzing hierarchical relationships or illustrating the flow of information, pyramid graphs are an excellent choice for visualizing data. We demonstrate some properties of the newly introduced graph such as chromatic polynomial which has many applications in discreet mathematics, in computer science and study the phase transitions in statistical physics models. Also discussed chromatic index, chromatic number, isomorphism, girth of the graph, edge and vertex connectivity and different theorems. Results on different types of dominations of the pyramid graph, the number of vertices in the least ordered set determines the domination of C which, identifies all specific vertices that dominate all vertices of the pyramid graph.