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In this paper we compute the Galois group of all minimally rigid graphs that can be constructed from a single edge by repeated Henneberg 1-steps. It turns out that any such group is totally imprimitive, i.e., it is determined by all the partitions it preserves.<\/jats:p>","DOI":"10.1007\/s00454-024-00711-4","type":"journal-article","created":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T10:13:53Z","timestamp":1736590433000},"page":"1105-1121","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Galois Groups of Type-1 Minimally Rigid Graphs"],"prefix":"10.1007","volume":"75","author":[{"given":"Mehdi","family":"Makhul","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Josef","family":"Schicho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1705-3873","authenticated-orcid":false,"given":"Audie","family":"Warren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,1,11]]},"reference":[{"issue":"2","key":"711_CR1","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1112\/S0010437X18007868","volume":"155","author":"A Esterov","year":"2019","unstructured":"Esterov, A.: Galois theory for general systems of polynomial equations. 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