Any part of a plat may be vacated under the provisions and subject to the conditions of this chapter if such does not abridge or destroy any of the rights and privileges of other proprietors in such plat.
Nothing contained in this section shall authorize the closing or obstructing of any public highways laid out according to law.
When any part of a plat shall be vacated as aforesaid, the proprietors of the lots so vacated may inclose the streets, alleys, and public grounds adjoining such lots in equal proportion.
SDCL 11-3-17