The interplay between the formation of neutron skin and alpha cluster at the dilute surface of neutron-rich nuclei is one of the interesting subjects in the study of neutron-rich nuclei and nuclear clustering. A theoretical model has predicted that the growth of neutron skin will prevent the alpha clustering at the nuclear surface. Quite recently, this theoretical perspective; the suppression of alpha clustering by the neutron-skin formation was first confirmed experimentally in Sn isotopes as the reduction of the (p, p alpha) reaction cross-section. Motivated by the novel discovery, in this work, we have investigated the relationship between the neutron-skin thickness and alpha clustering in C isotopes. Based on the analysis by the antisymmetrized molecular dynamics, we show that the alpha spectroscopic factor at nuclear exterior decreases in neutron-rich C isotopes, and the clustering suppression looks correlated with the growth of the neutron-skin thickness.
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