{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:07:38Z","timestamp":1753880858936,"version":"3.41.2"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"Department of Science and Technology of Henan","award":["HNGD2022060"],"award-info":[{"award-number":["HNGD2022060"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971054"],"award-info":[{"award-number":["11971054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p> Given a connected graph [Formula: see text] and [Formula: see text] with [Formula: see text], an [Formula: see text]-tree is a such subgraph [Formula: see text] of [Formula: see text] that is a tree with [Formula: see text]. Two [Formula: see text]-trees [Formula: see text] and [Formula: see text] are edge-disjoint if [Formula: see text]. Let [Formula: see text] be the maximum size of a set of edge-disjoint [Formula: see text]-trees in [Formula: see text]. The [Formula: see text]-connectivity of [Formula: see text] is defined as [Formula: see text]. In this paper, we first show some structural properties of edge-disjoint [Formula: see text]-trees by Fan Lemma and K\u00f6nig-ore Formula. Then, the [Formula: see text]-connectivity of the Cartesian product of trees is determined. That is, let [Formula: see text] be trees, then [Formula: see text] if [Formula: see text] for each [Formula: see text], otherwise [Formula: see text]. As corollaries, [Formula: see text]-connectivity for some graph classes such as hypercubes and meshes can be obtained directly. <\/jats:p>","DOI":"10.1142\/s0219265922500074","type":"journal-article","created":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T04:20:06Z","timestamp":1673324406000},"source":"Crossref","is-referenced-by-count":0,"title":["The \u03bb4-Connectivity of the Cartesian Product of Trees"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1132-8410","authenticated-orcid":false,"given":"Hengzhe","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, P. R. 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