Fast recognition of some parametric graph families

08/20/2020

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by   Nina Klobas, et al.

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We identify all [1, λ, 8]-cycle regular I-graphs and all [1, λ, 8]-cycle regular double generalized Petersen graphs. As a consequence we describe linear recognition algorithms for these graph families. Using structural properties of folded cubes we devise a o(N log N) recognition algorithm for them. We also study their [1,λ,4], [1,λ,6] and [2, λ, 6]-cycle regularity and settle the value of parameter λ.