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 at left above, both of which have graph spectrum (-2)0^3 2. Regular cospectral graphs are of particular interest, and the smallest regular graphs are the two pairs of quartic graphs illustrated above center and right (Cvetković et al. 1998, p. 398; van Dam and Haemers 2003). The first example of cospectral graphs was found by Collatz and Sinogowitz. Many examples are given in Cvetkovic et al. (1998, pp. 156-161) and Rücker et al. (2002).
