Coronae graphs and their $\alpha$-eigenvalues

Abstract

Let $G_1$ and $G_2$ be two simple connected graphs. The invariant \textit{coronal} of graph is used in order to determine the $\alpha$-eigenvalues of four different types of graph equations that are $G_1 \circ G_2, G_1\lozenge G_1$ and the other two`s are $G_1 \odot G_2$ and $G_1 \circleddash G_2$ which are obtained using the $R$-graph of $G_1$. As an application we construct infinitely many pairs of non-isomorphic $\alpha$-Isospectral graph.