{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:25:34Z","timestamp":1760239534629,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T00:00:00Z","timestamp":1606262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basic Science Research Program through the National Research Foundation of Korea  (NRF)","award":["(2018R1D1A1B05048450) and (2020R1I1A3A04036669)"],"award-info":[{"award-number":["(2018R1D1A1B05048450) and (2020R1I1A3A04036669)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An efficient total dominating set D of a graph G is a vertex subset such that every vertex of G has exactly one neighbor in the set D. In this paper, we give necessary and sufficient conditions for the existence of efficient total domination sets of circulant graphs whose degree is 5 and classify these sets.<\/jats:p>","DOI":"10.3390\/sym12121944","type":"journal-article","created":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T21:55:06Z","timestamp":1606341306000},"page":"1944","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Classification of Efficient Total Domination Sets of Circulant Graphs of Degree 5"],"prefix":"10.3390","volume":"12","author":[{"given":"Young Soo","family":"Soo Kwon","sequence":"first","affiliation":[{"name":"Department of Mathematics, Yeungnam University, Kyongsan 712-749, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moo Young","family":"Young Sohn","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Changwon National University, Changwon 641-773, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Haynes, T.W., Hedetniemi, S.T., and Slater, P.J. 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