isospectral graphs

Cospectral graphs, also called isospectral graphs, are graphs that share the same graph spectrum. The smallest pair of isospectral graphs is the graph union C_4 union K_1 and star graph S_5, illustrated above, both of which have graph spectrum (-2)0^3 2. The first example was found by Collatz and Sinogowitz. Many examples are given in Cvetkovic et al. (1998, pp. 156-161) and Rücker et al. (2002). The smallest pair of cospectral graphs is the graph union C_4 union K_1 and star graph S_5, illustrated above, both of which have graph spectrum (-2)0^3 2. The following table summarizes some prominent named cospectral graphs.

determined by spectrum | graph eigenvalue | graph spectrum | Hoffman graph | isospectral manifolds | Shrikhande graph