{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T04:25:53Z","timestamp":1784694353540,"version":"3.55.0"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T00:00:00Z","timestamp":1573776000000},"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\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2019YJS192"],"award-info":[{"award-number":["2019YJS192"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,1,19]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The generalized $k$-connectivity of a graph $G$ is a parameter that can measure the reliability of a network $G$ to connect any $k$ vertices in $G$, which is a generalization of traditional connectivity. Let $S\\subseteq V(G)$ and $\\kappa _{G}(S)$ denote the maximum number $r$ of edge-disjoint trees $T_{1}, T_{2}, \\cdots , T_{r}$ in $G$ such that $V(T_{i})\\bigcap V(T_{j})=S$ for any $i, j \\in \\{1, 2, \\cdots , r\\}$ and $i\\neq j$. For an integer $k$ with $2\\leq k\\leq n$, the generalized $k$-connectivity of a graph $G$ is defined as $\\kappa _{k}(G)= min\\{\\kappa _{G}(S)|S\\subseteq V(G)$ and $|S|=k\\}$. In this paper, we introduce a family of regular graph $G_{n}$ that can be constructed recursively and each vertex with exactly one outside neighbor. The generalized $3$-connectivity of the regular graph $G_{n}$ is studied, which attains a previously proven upper bound on $\\kappa _{3}(G)$. As applications of the main result, the generalized $3$-connectivity of some important networks including some known results such as the alternating group network $AN_{n}$, the star graph $S_{n}$ and the pancake graphs $P_{n}$ can be obtained directly.<\/jats:p>","DOI":"10.1093\/comjnl\/bxz116","type":"journal-article","created":{"date-parts":[[2019,8,28]],"date-time":"2019-08-28T11:42:19Z","timestamp":1566992539000},"page":"1-6","source":"Crossref","is-referenced-by-count":13,"title":["Reliability Assessment of Some Regular Networks"],"prefix":"10.1093","volume":"64","author":[{"given":"Shu-Li","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rong-Xia","family":"Hao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P.R. 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