{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T14:22:04Z","timestamp":1698330124240},"reference-count":8,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,12,19]],"date-time":"2006-12-19T00:00:00Z","timestamp":1166486400000},"content-version":"vor","delay-in-days":4492,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory &amp; Apps"],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Up to now the theory of infinite and transfinite graphs and electrical networks has been established only for the case where the branch sets are countable. This work extends that prior theory to graphs and networks with uncountable branch sets, a structure that arises quite naturally in the theory of transfinite graphs. Moreover, conditions on the local structure of the transfinite graph are given which insure the countability of the branch set. Finally, it is shown that only countably many of the branches in an uncountable electrical network can have non\u2010zero voltages and currents, and therefore the restriction to countability in the prior theory is not essentially restrictive.<\/jats:p>","DOI":"10.1002\/cta.4490220507","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T11:23:17Z","timestamp":1183375397000},"page":"387-398","source":"Crossref","is-referenced-by-count":1,"title":["Uncountable transfinite graphs and electrical networks"],"prefix":"10.1002","volume":"22","author":[{"given":"A. H.","family":"Zemanian","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,12,19]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490030403"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511895432"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2153970"},{"key":"e_1_2_1_5_2","volume-title":"The Theory of Sets and Transfinite Arithmetic","author":"Abian A.","year":"1965"},{"key":"e_1_2_1_6_2","unstructured":"A. H.Zemanian Uncountable transfinite graphs and electrical networks CEAS Tech. Rep. 670 University at Stony Brook 1993."},{"key":"e_1_2_1_7_2","unstructured":"A. H.Zemanian Connectedness in transfinite graphs and the existence and uniqueness of node voltages Discrete Math. in press."},{"key":"e_1_2_1_8_2","volume-title":"Introduction to Graph Theory","author":"Wilson R. J.","year":"1972"},{"key":"e_1_2_1_9_2","volume-title":"Methodes Mathematiques pour les Sciences Physiques","author":"Schwartz L.","year":"1961"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.4490220507","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.4490220507","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T23:26:56Z","timestamp":1698103616000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.4490220507"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":8,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1994,9]]}},"alternative-id":["10.1002\/cta.4490220507"],"URL":"https:\/\/doi.org\/10.1002\/cta.4490220507","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}