Spectral Characterization of Some Generalized Odd Graphs

Abstract

Suppose G is a connected, k-regular graph such that SpecOGUaSpecOGU where G is a distance-regular graph of diameter d with parameters a1a a2aa adˇ1a 0 and ad > 0; i.e., a generalized odd graph, we show that G must be distance-regular with the same intersection array as that of G in terms of the notion of Homan Polynomials. Fur- thermore, G is isomorphic to G if G is one of the odd polygon C2da1, the Odd graph Oda1, the folded O2da 1U-cube, the coset graph of binary Golay code Oda 3U, the Homan- Singleton graphOda 2U, the Gewirtz graphOda 2U, the Higman-Sims graphOda 2U ,o r the second subconstituent of the Higman-Sims graphOda 2U.