Fast recognition of some parametric graph families

Abstract

We identify all [1, λ, 8]-cycle regular I-graphs, all [1, λ, 8]-cycle regular double generalized Petersen graphs, and the unique [1, λ, 6]-cycle regular folded hypercube. As a consequence we describe linear recognition algorithms for the first two graph families, and a quasilinear recognition algorithm for the folded hypercubes.