{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:17:18Z","timestamp":1761178638099,"version":"build-2065373602"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"10","license":[{"start":{"date-parts":[[2025,5,18]],"date-time":"2025-05-18T00:00:00Z","timestamp":1747526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"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"}]},{"name":"Fujian Alliance of Mathematics","award":["2025SXLMMS03"],"award-info":[{"award-number":["2025SXLMMS03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Analysis of the reliability of networks is crucial to the design and optimization of networks. The $P$-conditional edge-connectivity $\\lambda (P;G)$ of a network $G$ is the minimum number of edges whose deletion will divide $G$ into several components, and each component satisfies the property $P$. It proposes a more pinpoint analysis to the reliability of networks. The paper investigates several different the $P$-conditional edge-connectivities of $K_{p;t}^{n}$, such as $d$-embedded edge-connectivity $\\lambda (P_{1}^{d};K_{p;t}^{n})$, $(t-1)pd$-good-neighbor edge-connectivity $\\lambda (P_{3}^{(t-1)pd};K_{p;t}^{n})$, $(t-1)pd$-average edge-connectivity $\\lambda (P_{4}^{(t-1)pd};K_{p;t}^{n})$ for $t\\geq 2$, $p\\geq 2$ and $0\\leq d\\leq n-1$, and they possess the same value $(t-1)p(n-d)(tp)^{d}$. Besides, we derive $\\lambda (P_{2}^{l}; K_{p;t}^{n})= (t-1)pnl-ex_{l}(K_{p;t}^{n})$ for $1\\leq l\\leq (tp)^{{\\lfloor \\frac{n}{2} \\rfloor }}$, where $ex_{l}(K_{p;t}^{n})$ denotes the twice of the maximum number of edges in a subgraph induced by $l$ vertices in $K_{p;t}^{n}$. Our method generalizes the result of Yu and Xu in (Comput J 2024; 67: 688\u201393) and Zhang et\u00a0al. in (J Supercomput 2022; 78: 7936\u201347).<\/jats:p>","DOI":"10.1093\/comjnl\/bxaf053","type":"journal-article","created":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T08:00:31Z","timestamp":1745740831000},"page":"1502-1509","source":"Crossref","is-referenced-by-count":0,"title":["Reliability analysis for the\n                    <i>n<\/i>\n                    th Cartesian product of the balanced complete multipartite graph under various hypotheses"],"prefix":"10.1093","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1393-4950","authenticated-orcid":false,"given":"Xuemin","family":"Wu","sequence":"first","affiliation":[{"name":"School of Science , Jimei University, Xiamen, Fujian 361021, PR","place":["China"]},{"name":"Digital Fujian Big Data Modeling and Intelligent Computing Institute , Jimei University, Xiamen, Fujian 361021, 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