On the eigenvalues of Cayley graphs on generalized dihedral groups

‎Let \Gamma be a graph with adjacency eigenvalues \lambda_۱\leq\lambda_۲\leq\ldots\leq\lambda_n‎. ‎Then the energy of‎ ‎\Gamma‎, ‎a concept defined in ۱۹۷۸ by Gutman‎, ‎is defined as \mathcal{E}(G)=\sum_{i=۱}^n|\lambda_i|‎. ‎Also‎ ‎the Estrada index of \Gamma‎, ‎which is defined in ۲۰۰۰ by Ernesto Estrada‎, ‎is defined as EE(\Gamma)=\sum_{i=۱}^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.

کلیدواژه ها:

‎Eigenvalue‎ ، ‎Energy of graph‎ ، ‎Estrada index‎ ، ‎Cayley graph‎ ، ‎Semi-Cayley graph