We investigate the single-molecule electrical conductance of alkane rings connected to gold electrodes and demonstrate that their logarithmic conductances are ocillatory functions of length. This contrasts with the logarithmic conductances of alkane chains, which decay linearly with length. This non-classical behaviour is attributed to conformational effects in the alkane rings, which tend to be more (less) planar when their branches contain even (odd) numbers of CH2 groups. Surprisingly the

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... ductances of alkane rings with two parallel conductance paths are predicted to be lower then those of the corresponding linear chains with only one conductance path