{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T20:27:03Z","timestamp":1769977623002,"version":"3.49.0"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"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"}]},{"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"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p> An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A connected graph [Formula: see text] is said to be maximally local-edge-connected if each pair of vertices [Formula: see text] and [Formula: see text] of [Formula: see text] are connected by [Formula: see text] pairwise edge-disjoint paths. In this paper, we show that the [Formula: see text]-dimensional augmented cube [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected and the bound [Formula: see text] is sharp; under the restricted condition that each vertex has at least three fault-free adjacent vertices, [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected and the bound [Formula: see text] is sharp; and under the restricted condition that each vertex has at least [Formula: see text] fault-free adjacent vertices, [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected. Furthermore, we show that a [Formula: see text]-regular graph [Formula: see text] is [Formula: see text]-fault-tolerant one-to-many maximally local-connected if [Formula: see text] does not contain [Formula: see text] and is super [Formula: see text]-vertex-connected of order\u00a01, a [Formula: see text]-regular graph [Formula: see text] is [Formula: see text]-fault-tolerant one-to-many maximally local-connected if [Formula: see text] does not contain [Formula: see text] and is super [Formula: see text]-vertex-connected of order\u00a01. <\/jats:p>","DOI":"10.1142\/s0129626420400010","type":"journal-article","created":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T07:38:43Z","timestamp":1602574723000},"page":"2040001","source":"Crossref","is-referenced-by-count":6,"title":["Fault-Tolerant Maximal Local-Edge-Connectivity of Augmented Cubes"],"prefix":"10.1142","volume":"30","author":[{"given":"Liyang","family":"Zhai","sequence":"first","affiliation":[{"name":"School of Science, Jimei University, Xiamen, Fujian, China"}]},{"given":"Liqiong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Science, Jimei University, Xiamen, Fujian, China"}]},{"given":"Weihua","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, China"}]}],"member":"219","published-online":{"date-parts":[[2020,10,12]]},"reference":[{"key":"S0129626420400010BIB001","doi-asserted-by":"publisher","DOI":"10.1080\/17445760.2012.735234"},{"key":"S0129626420400010BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"S0129626420400010BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2014.10.006"},{"key":"S0129626420400010BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.03.022"},{"key":"S0129626420400010BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2012.03.040"},{"key":"S0129626420400010BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.03.011"},{"key":"S0129626420400010BIB007","doi-asserted-by":"publisher","DOI":"10.1002\/net.10033"},{"key":"S0129626420400010BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.04.001"},{"key":"S0129626420400010BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.03.005"},{"key":"S0129626420400010BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2017.02.047"},{"key":"S0129626420400010BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2017.10.017"},{"key":"S0129626420400010BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2018.12.024"},{"key":"S0129626420400010BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2007.10.005"},{"key":"S0129626420400010BIB015","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"S0129626420400010BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(02)00600-5"},{"key":"S0129626420400010BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0219265903000763"},{"key":"S0129626420400010BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2016.09.002"},{"key":"S0129626420400010BIB020","doi-asserted-by":"publisher","DOI":"10.1142\/S021926590900256X"},{"key":"S0129626420400010BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2007.10.009"},{"key":"S0129626420400010BIB022","first-page":"564","volume-title":"6th International Conference on Information Technology: New Generations","author":"Shih L.-M."},{"key":"S0129626420400010BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2017.05.001"},{"key":"S0129626420400010BIB024","first-page":"4394","volume-title":"3rd International Congress on Image and Signal Processing","author":"Zhou S."}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626420400010","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T07:39:19Z","timestamp":1602574759000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626420400010"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":22,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1142\/S0129626420400010"],"URL":"https:\/\/doi.org\/10.1142\/s0129626420400010","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9]]}}}