{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:11:33Z","timestamp":1760242293272,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,22]],"date-time":"2017-03-22T00:00:00Z","timestamp":1490140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges. We are interested, for instance, in minimal numbers of edges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge) domination graphs are presented. Several open questions are posed.<\/jats:p>","DOI":"10.3390\/sym9030046","type":"journal-article","created":{"date-parts":[[2017,3,22]],"date-time":"2017-03-22T12:04:00Z","timestamp":1490184240000},"page":"46","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetry in Domination for Hypergraphs with Choice"],"prefix":"10.3390","volume":"9","author":[{"given":"Kenneth","family":"S. Berenhaut","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC 27106, USA"}]},{"given":"Brendan","family":"P. Lidral-Porter","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC 27106, USA"}]},{"given":"Theodore","family":"H. 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