{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T20:29:23Z","timestamp":1773260963683,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T00:00:00Z","timestamp":1686787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSF","award":["DMS-1916494"],"award-info":[{"award-number":["DMS-1916494"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The topological symmetry group of an embedding \u0393 of an abstract graph \u03b3 in S3 is the group of automorphisms of \u03b3 that can be realized by homeomorphisms of the pair (S3,\u0393). These groups are motivated by questions about the symmetries of molecules in space. The Petersen family of graphs is an important family of graphs for many problems in low-dimensional topology, so it is desirable to understand the possible groups of symmetries of their embeddings in space. In this paper, we find all the groups that can be realized as topological symmetry groups for each of the graphs in the Petersen family. Along the way, we also complete the classification of the realizable topological symmetry groups for K3,3.<\/jats:p>","DOI":"10.3390\/sym15061267","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T01:31:31Z","timestamp":1686879091000},"page":"1267","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Topological Symmetry Groups of the Petersen Graphs"],"prefix":"10.3390","volume":"15","author":[{"given":"Deion","family":"Elzie","sequence":"first","affiliation":[{"name":"Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samir","family":"Fridhi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Loyola Marymount University, 1 LMU Drive, Los Angeles, CA 90045, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Blake","family":"Mellor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Loyola Marymount University, 1 LMU Drive, Los Angeles, CA 90045, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Silva","sequence":"additional","affiliation":[{"name":"Department of Mathematics, California State Polytechnic University, 3801 West Temple Ave., Pomona, CA 91768, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robin T.","family":"Wilson","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Loyola Marymount University, 1 LMU Drive, Los Angeles, CA 90045, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0040-9383(86)90041-8","article-title":"Topological chirality of certain molecules","volume":"25","author":"Simon","year":"1986","journal-title":"Topology"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Flapan, E. 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