{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:19:05Z","timestamp":1760710745214},"reference-count":16,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T00:00:00Z","timestamp":1634428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"General Project of Hunan Provincial Education Department of China","award":["19C1742"],"award-info":[{"award-number":["19C1742"]}]},{"name":"Youth Project of Hunan Provincial Natural Science Foundation of China","award":["2021JJ40522"],"award-info":[{"award-number":["2021JJ40522"]}]},{"name":"Hu Xiang Gao Ceng Ci Ren Cai Ju Jiao Gong Cheng-Chuang Xin Ren Cai","award":["2019RS1057"],"award-info":[{"award-number":["2019RS1057"]}]},{"name":"Project of Scientific Research Fund of Hunan Provincial Science and Technology Department","award":["2018WK4006"],"award-info":[{"award-number":["2018WK4006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,2,19]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A bipartite graph is Hamiltonian laceable if any two of its vertices in different partite sets are connected by a Hamiltonian path. A Hamiltonian laceable graph $G$ is called strongly Hamiltonian laceable if any two of its vertices in the same partite set are connected by a path of length $|V(G)|-2$. A Hamiltonian laceable graph $G$ (with two partite sets $V_0, V_1$) is called hyper-Hamiltonian laceable, if for any vertex $v \\in V_{i}$ for $i \\in \\{0,1\\}$, there is a Hamiltonian path of $G-\\{v\\}$ between any two vertices in $V_{1-i}$. In this paper, we focus on the edge-fault-tolerant strongly Hamiltonian laceability and hyper-Hamiltonian laceability on the class of Cayley graphs generated by transposition trees, which are a generalization of star graph and bubble-sort graph. For every $n$-dimensional Cayley graph generated by a transposition tree $\\Gamma _n$, we show that $\\Gamma _{n}-F$ is strongly Hamiltonian laceable for any $F \\subseteq E(\\Gamma _{n})$ with $|F|\\leq n-3$, which generalizes results in [ 1, 11], and show that $\\Gamma _{n}-F$ is hyper-Hamiltonian laceable for any $F \\subseteq E(\\Gamma _{n})$ with $|F|\\leq n-4$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxab167","type":"journal-article","created":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T11:35:32Z","timestamp":1634038532000},"page":"384-398","source":"Crossref","is-referenced-by-count":9,"title":["Fault-Tolerant Strongly Hamiltonian Laceability and Hyper-Hamiltonian Laceability of Cayley Graphs Generated by Transposition Trees"],"prefix":"10.1093","volume":"66","author":[{"given":"Shudan","family":"Xue","sequence":"first","affiliation":[{"name":"Key Laboratory of Intelligent Computing Information Processing of Education School of Mathematics and Computational Science , Xiangtan University, Xiangtan, Hunan 411105, PR China"}]},{"given":"Qingying","family":"Deng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing Information Processing of Education School of Mathematics and Computational Science , Xiangtan University, Xiangtan, Hunan 411105, PR China"}]},{"given":"Pingshan","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Computing Information Processing of Education School of Mathematics and Computational Science , Xiangtan University, Xiangtan, Hunan 411105, PR China"}]}],"member":"286","published-online":{"date-parts":[[2021,10,17]]},"reference":[{"key":"2023022013493619500_","doi-asserted-by":"crossref","first-page":"2679","DOI":"10.1016\/j.ins.2007.01.017","article-title":"Hamiltonian laceability of bubble-sort graphs with edge faults","volume":"177","author":"Araki","year":"2007","journal-title":"Inf. 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