Eccentric Graph of Join of Graphs

The eccentric graph \({G}_{e}\) corresponding to a graph \(G\) is a derived graph with the same vertex set of \(G\) and two vertices in \({G}_{e}\) are neighbours if one of them is the eccentric vertex of the other. Motivated by the studies on derived graphs and graph operations, in this article, the eccentric graph of the join of two graphs is analysed based on the variations in the radius. The notion of eccentric join of two graphs with at least one of them having radius \(1\), is introduced. The eccentric graph of eccentric join of graphs is also examined. Finally, the concept of r-eccentric join of graphs is also introduced. This study is analytical in nature, which involves deductive and logical reasoning.