Spectral techniques are used for the study of several network properties: community detection, bipartition, clustering, design of highly synchronizable networks, and so forth. In this paper, we investigate which kinds of bicyclic networks are determined by their per-spectra. We find that the permanental spectra cannot determine sandglass graphs in general. When we restrict our consideration to connected graphs or quadrangle-free graphs, sandglass graphs are determined by their permanental spectra. Furthermore, we construct countless pairs of per-cospectra bicyclic networks.
"Per-Spectral Characterizations of Bicyclic Networks." J. Appl. Math. 2017 1 - 5, 2017. https://doi.org/10.1155/2017/7541312