{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:53:57Z","timestamp":1760151237896,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,2,25]],"date-time":"2022-02-25T00:00:00Z","timestamp":1645747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801494, 11961007"],"award-info":[{"award-number":["11801494, 11961007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Technology Foundation of Guizhou Province","award":["[2020]1Y405"],"award-info":[{"award-number":["[2020]1Y405"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let R be a finite ring. In this paper, we mainly explore the conditions to ensure the graph B\u0393n defined by a system of equations {fi|i=2,\u2026,n} to be a Cayley graph or a Hamiltonian graph. More precisely, we prove that B\u0393n is a Cayley graph with G=\u27e8\u03d5,A\u27e9 a group of dihedral type if and only if the system Fn={fi|i=2,\u2026,n} is Cayley graphic of dihedral type in R. As an application, the well-known Lova\u00b4sz Conjecture, which states that any finite connected Cayley graph has a Hamilton cycle, holds for the connected B\u0393n defined by Cayley graphic system Fn of dihedral type in the field GF(pk).<\/jats:p>","DOI":"10.3390\/axioms11030100","type":"journal-article","created":{"date-parts":[[2022,2,25]],"date-time":"2022-02-25T10:00:40Z","timestamp":1645783240000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cayley Graphs Defined by Systems of Equations"],"prefix":"10.3390","volume":"11","author":[{"given":"Fuyuan","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8990-9610","authenticated-orcid":false,"given":"Qiang","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Yangzhou University, Yangzhou 225002, China"}]},{"given":"Hongbo","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Guiyang University, Guiyang 550005, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1030-7279","authenticated-orcid":false,"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1006\/eujc.1993.1048","article-title":"New examples of graphs without small cycles and of large size","volume":"14","author":"Lazebnik","year":"1993","journal-title":"Eur. 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