{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T05:40:23Z","timestamp":1695879623929},"reference-count":4,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":6158,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1989,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper considers the following variation on the construction of a reliable communication network. Whenever a vertex is attacked, all vertices within distance 2 are also destroyed (or fail) indirectly. We are interested in designing a connected graph (undirected, all edges of length one) on <jats:italic>p<\/jats:italic> vertices such that when a random subset of the vertices are attacked the expected number of vertices that are destroyed (directly and indirectly) is minimized. It is assumed that any of the 2<jats:sup>p<\/jats:sup> subsets of vertices is equally likely to be attacked. The optimal structure is determined for all <jats:italic>p<\/jats:italic> and is shown to be one of five patterns depending on <jats:italic>r<\/jats:italic> where <jats:italic>p<\/jats:italic> = 5t + r.<\/jats:p>","DOI":"10.1002\/net.3230190704","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T06:16:53Z","timestamp":1178950613000},"page":"771-792","source":"Crossref","is-referenced-by-count":5,"title":["On designing a network to defend against random attacks of radius two"],"prefix":"10.1002","volume":"19","author":[{"given":"A. S.","family":"Finbow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B. L.","family":"Hartnell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"G.GuntherandB. L.Hartnell On minimizing the effects of betrayals in a resistance movement.Proceedings of the Eight Manitoba Conference on Numerical Mathematics and Computing(1978)285\u2013306."},{"key":"e_1_2_1_3_2","unstructured":"B. L.Hartnell The optimum defense against random subversions in a network.Proceedings of the Tenth Southeastern Conference on Combinatorics Graph Theory and ComputingBoca Raton FL (April1979)293\u2013299."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230160106"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.18.1.1"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230190704","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230190704","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T07:33:41Z","timestamp":1695800021000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230190704"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,12]]},"references-count":4,"journal-issue":{"issue":"7","published-print":{"date-parts":[[1989,12]]}},"alternative-id":["10.1002\/net.3230190704"],"URL":"https:\/\/doi.org\/10.1002\/net.3230190704","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,12]]}}}