{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:40:38Z","timestamp":1698043238291},"reference-count":9,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":5788,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1990,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Two source\u2010sink (directed) networks are called <jats:italic>path\u2010isomorphic<\/jats:italic> if there exists a bijection \u03c0 between their arc sets that preserves (simple) source\u2010sink directed paths. Although path\u2010isomorphic networks need not be isomorphic (they need not even have the same number of nodes), we show that several properties are preserved. For example, suppose <jats:italic>N<\/jats:italic> and <jats:italic>N\u2032<\/jats:italic> are path\u2010isomorphic. Then, <jats:italic>N<\/jats:italic> is acyclic if and only if <jats:italic>N\u2032<\/jats:italic> is acyclic. <jats:italic>B<\/jats:italic> is the arc set of block of <jats:italic>N<\/jats:italic> if and only if \u03c0(<jats:italic>B<\/jats:italic>) is the arc set of a block of <jats:italic>N\u2032<\/jats:italic>. Also, <jats:italic>D<\/jats:italic> is the arc set of a dicomponent of <jats:italic>N<\/jats:italic> if and only if \u03c0(<jats:italic>D<\/jats:italic>) is the arc set of a dicomponent of <jats:italic>N\u2032.<\/jats:italic> In addition, we prove a dipath version of Whitney's well\u2010known 2\u2010isomorphism theorem for a special class of networks, which includes the acyclic networks.<\/jats:p>","DOI":"10.1002\/jgt.3190140611","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:50:29Z","timestamp":1181285429000},"page":"709-722","source":"Crossref","is-referenced-by-count":0,"title":["Path\u2010isomorphic networks"],"prefix":"10.1002","volume":"14","author":[{"given":"David","family":"Hartvigsen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400875184"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584085"},{"key":"e_1_2_1_4_2","unstructured":"D.Hartvigsen Recognizing classes of path\u2010arc incidence matrices. Working paper (1987)."},{"key":"e_1_2_1_5_2","unstructured":"D.Hartvigsen Whitney\u2010type theorems for s\u2010t networks. Working paper (1987)."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0112059"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"e_1_2_1_8_2","unstructured":"P. D.SeymourandC.Thomassen Characterization of even digraphs. Preprint (1984)."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(89)90050-6"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2371127"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190140611","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190140611","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:32:30Z","timestamp":1697999550000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190140611"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,12]]},"references-count":9,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1990,12]]}},"alternative-id":["10.1002\/jgt.3190140611"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190140611","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,12]]}}}