Per-Spectral Characterizations of Bicyclic Networks

Abstract EN

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.