On the eigenvalues of Cayley graphs on generalized dihedral groups

Document Type : Research Paper


1 ‎Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj‎, ‎Iran.

2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran



‎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.


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