{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:00:14Z","timestamp":1740142814076,"version":"3.37.3"},"reference-count":27,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T00:00:00Z","timestamp":1573603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301217"],"award-info":[{"award-number":["11301217"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2018J01419"],"award-info":[{"award-number":["2018J01419"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]},{"name":"New Century Excellent Talents in Fujian Province University","award":["JA14168"],"award-info":[{"award-number":["JA14168"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,8,20]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let $G=(V(G), E(G))$ be a connected graph. A subset $T \\subseteq V(G)$ is called an $R^{k}$-vertex-cut, if $G-T$ is disconnected and each vertex in $V(G)-T$ has at least $k$ neighbors in $G-T$. The cardinality of a minimum $R^{k}$-vertex-cut is the $R^{k}$-vertex-connectivity of $G$ and is denoted by $\\kappa ^{k}(G)$. $R^{k}$-vertex-connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study $R^{1}$-vertex-connectivity and $R^{2}$-vertex-connectivity of Cayley graphs generated by wheel graphs, which are denoted by $AW_{n}$, and show that $\\kappa ^{1}(AW_{n})=4n-7$ for $n\\geq 6$; $\\kappa ^{2}(AW_{n})=6n-12$ for $n\\geq 6$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxz077","type":"journal-article","created":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T11:08:32Z","timestamp":1562670512000},"page":"1372-1384","source":"Crossref","is-referenced-by-count":0,"title":["A Kind Of Conditional Vertex Connectivity Of Cayley Graphs Generated By Wheel Graphs"],"prefix":"10.1093","volume":"63","author":[{"given":"Zuwen","family":"Luo","sequence":"first","affiliation":[{"name":"School of Science, Jimei University, Xiamen, Fujian 361021, PR China"}]},{"given":"Liqiong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Science, Jimei University, Xiamen, Fujian 361021, PR China"}]}],"member":"286","published-online":{"date-parts":[[2019,11,13]]},"reference":[{"key":"2020091506341519000_ref1","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.1109\/12.42131","article-title":"Generalized measures of fault tolerance with application to n-cube networks","volume":"38","author":"Esfahanian","year":"1989","journal-title":"IEEE Trans. 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