{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T21:12:34Z","timestamp":1778274754141,"version":"3.51.4"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T00:00:00Z","timestamp":1610064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P30031"],"award-info":[{"award-number":["P30031"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of\u00a0Hunan Province","doi-asserted-by":"publisher","award":["2020JJ4675"],"award-info":[{"award-number":["2020JJ4675"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper considers commuting graphs over the semidihedral group SD8n. We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n\u226515 or even n\u22652. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n. We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.<\/jats:p>","DOI":"10.3390\/sym13010103","type":"journal-article","created":{"date-parts":[[2021,1,10]],"date-time":"2021-01-10T23:03:42Z","timestamp":1610319822000},"page":"103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Properties of Commuting Graphs over Semidihedral Groups"],"prefix":"10.3390","volume":"13","author":[{"given":"Tao","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8454-5857","authenticated-orcid":false,"given":"Matthias","family":"Dehmer","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Swiss Distance University of Applied Sciences, 3900 Brig, Switzerland"},{"name":"College of Artificial Intelligence, Nankai University, Tianjin 300350, China"},{"name":"School of Sciences, Xi\u2019an Technological University, Xi\u2019an 710021, China"},{"name":"Department of Biomedical Computer Science and Mechatronics, UMIT, A-6060 Hall in Tyrol, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Emmert-Streib","sequence":"additional","affiliation":[{"name":"Predictive Medicine and Data Analytics Lab, Department of Signal Processing, Tampere University, 33100 Tampere, Finland"},{"name":"Institute of Biosciences and Medical Technology, 33520 Tampere, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongtao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hunan University, Changsha 410082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weijun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, New Campus, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/j.jcta.2005.09.003","article-title":"The connectivity of commuting Graphs","volume":"113","author":"Bundy","year":"2006","journal-title":"J. Combin. Theory Ser. A"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ali, F., and Li, Y. (2019). The connectivity and the spectral radius of commuting graphs on certain finite groups. Linear Multilinear Algebra.","DOI":"10.1080\/03081087.2019.1700893"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.laa.2019.01.002","article-title":"Integral Cayley graphs over dicyclic group","volume":"566","author":"Cheng","year":"2019","journal-title":"Linear Algebra Appl."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cheng, T., Feng, L., and Liu, W. (2019). Directed Strongly Regular Cayley Graphs over Metacyclic Groups of Order 4n. Mathematics, 7.","DOI":"10.3390\/math7111011"},{"key":"ref_5","first-page":"1","article-title":"The energy of a graph","volume":"103","author":"Gutman","year":"1978","journal-title":"Ber. Math. Stat. Sekt. Forschungszent. 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An Introduction to the Theory of Graph Spectra, Cambridge University Prese.","DOI":"10.1017\/CBO9780511801518"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Brouwer, A.E., and Haemers, W.H. (2012). Spectra of Graphs, Springer.","DOI":"10.1007\/978-1-4614-1939-6"},{"key":"ref_13","unstructured":"West, D.B. (2003). Introduction to Graph Theory, Prentice-Hall."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/103\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:08:35Z","timestamp":1760159315000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,8]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010103"],"URL":"https:\/\/doi.org\/10.3390\/sym13010103","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,8]]}}}