{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T16:02:06Z","timestamp":1773244926068,"version":"3.50.1"},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4301,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The stability of a (communication or transportation) network composed of (processing) nodes and (communication or transportation) links is of prime importance to network designers. As the network begins losing links or nodes, eventually, there is a loss in its effectiveness. Thus, it is desirable that networks be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconfiguration of the network after disruption. Many graph theoretical parameters have been used in the past to describe the stability of networks, including the vertex\u2010connectivity and edge\u2010connectivity, toughness and edge\u2010toughness, integrity and edge\u2010integrity, and tenacity. In this paper, we study the edge\u2010tenacity of graphs. We will be primarily interested in edge\u2010tenacious graphs, which can be considered very stable and are somewhat analogous in edge\u2010tenacity to honest graphs in edge\u2010integrity. We prove several results about edge\u2010tenacious graphs as well as find numerous classes of edge\u2010tenacious graphs.<\/jats:p>","DOI":"10.1002\/net.3230250103","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T19:18:00Z","timestamp":1178997480000},"page":"7-17","source":"Crossref","is-referenced-by-count":28,"title":["Edge\u2010tenacious networks"],"prefix":"10.1002","volume":"25","author":[{"given":"Barry L.","family":"Piazza","sequence":"first","affiliation":[]},{"given":"Fred S.","family":"Robertst","sequence":"additional","affiliation":[]},{"given":"Sam K.","family":"Stueckle","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"141","article-title":"On the edge\u2010integrity of graphs","volume":"60","author":"Bagga K. S.","year":"1987","journal-title":"Congr. Numer."},{"key":"e_1_2_1_3_2","first-page":"103","article-title":"Integrity of trees and powers of cycles","volume":"58","author":"Barefoot C. A.","year":"1987","journal-title":"Congr. Numer."},{"key":"e_1_2_1_4_2","first-page":"13","article-title":"Vulnerability in graphs\u2013A comparative survey","volume":"1","author":"Barefoot C. A.","year":"1987","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"e_1_2_1_5_2","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"1986"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(73)90138-6"},{"key":"e_1_2_1_7_2","series-title":"Proceedings of the Seventh Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms and Applications","volume-title":"The tenacity of a graph","author":"Cozzens M."},{"key":"e_1_2_1_8_2","unstructured":"J.Fetterman personal communication."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.48.7.1142"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230250103","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230250103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T05:32:41Z","timestamp":1698298361000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230250103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/net.3230250103"],"URL":"https:\/\/doi.org\/10.1002\/net.3230250103","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}