On the eigenvalues of Cayley graphs on generalized dihedral groups
نویسندگان
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
doi
10.22034/as.2019.1481چکیده
Let $\Gamma$ be a graph with adjacency eigenvalues $\lambda_1\leq\lambda_2\leq\ldots\leq\lambda_n$. Then the energy of $\Gamma$, a concept defined in 1978 by Gutman, is defined as $\mathcal{E}(G)=\sum_{i=1}^n|\lambda_i|$. Also the Estrada index of $\Gamma$, which is defined in 2000 by Ernesto Estrada, is defined as $EE(\Gamma)=\sum_{i=1}^ne^{\lambda_i}$.In this paper, we compute the eigenvalues, energy and Estrada index of Cayley graphs on generalized dihedral groups. As an application, we compute these items for honeycomb toroidal graphs and Cayley graphs on dihedral groups.
