Vertex isoperimetry on signed graphs and spectra of non-bipartite Cayley and Cayley sum graphs

Chunyang Hu, Shiping Liu

For a non-bipartite finite Cayley graph, we show the non-trivial eigenvalues of its normalized adjacency matrix lie in the interval $$\left[-1+\frac{ch_{out}^2}{d},1-\frac{Ch_{out}…