Spectral characterization of odd graphs \(O_ k, k\leq 6\) (Q1340122)

The odd graph \(O_ k\), where \(k\geq 2\), has the \((k- 1)\)-subsets of \(\{1,2,\dots, 2k- 1\}\) as its vertices; and two such vertices are adjacent if and only if the corresponding subsets are disjoint. The author shows that if \(2\leq k\leq 6\) and \(\Gamma\) is a connected regular graph with the same spectrum as \(O_ k\), then \(\Gamma\) and \(O_ k\) are isomorphic.