{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T05:11:32Z","timestamp":1775625092580,"version":"3.50.1"},"reference-count":23,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1991,3,1]],"date-time":"1991-03-01T00:00:00Z","timestamp":667785600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":8174,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Applied Mathematics"],"published-print":{"date-parts":[[1991,3]]},"DOI":"10.1016\/0166-218x(91)90031-q","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T03:43:01Z","timestamp":1027654981000},"page":"37-49","source":"Crossref","is-referenced-by-count":19,"title":["Uniqueness of currents in infinite resistive networks"],"prefix":"10.1016","volume":"31","author":[{"given":"Paolo M.","family":"Soardi","sequence":"first","affiliation":[]},{"given":"Wolfgang","family":"Woess","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0166-218X(91)90031-Q_BIB1","first-page":"107","article-title":"A local limit theorem for random walks on the cartesian product of discrete groups","volume":"A","author":"Cartwright","year":"1987","journal-title":"Boll. Un. Mat. Ital."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB2","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1090\/S0002-9947-1984-0743744-X","article-title":"Isoperimetric inequality and transience of certain random walks","volume":"284","author":"Dodziuk","year":"1984","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB3","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/TCT.1971.1083286","article-title":"Infinite electrical networks: I \u2014 resistive networks","volume":"18","author":"Flanders","year":"1971","journal-title":"IEEE Trans. Circuit Theory"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB4","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0022-247X(72)90026-1","article-title":"Infinite electrical networks: II \u2014 resistance in an infinite grid","volume":"40","author":"Flanders","year":"1972","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02566233","article-title":"\u00dcber die Enden diskreter R\u00e4ume und Gruppen","volume":"17","author":"Freudenthal","year":"1944","journal-title":"Comment. Math. Helv."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB6","first-page":"49","article-title":"Eine isoperimetrische Eigenschaft von B\u00e4umen","volume":"195","author":"Gerl","year":"1986","journal-title":"Sitzungsber. \u00d6st. Akad. Wiss. Math.-Natur. Kl."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB7","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/BF01046933","article-title":"Random walks on a graph with a strong isoperimetric property","volume":"1","author":"Gerl","year":"1988","journal-title":"J. Theoret. Probab."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB8","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/BF01788688","article-title":"A note on bounded automorphisms of infinite graphs","volume":"5","author":"Godsil","year":"1989","journal-title":"Graphs Combin."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB9","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF01362670","article-title":"\u00dcber unendliche Wege in Graphen","volume":"157","author":"Halin","year":"1964","journal-title":"Math. Ann."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB10","first-page":"251","article-title":"Endomorphisms and automorphisms of infinite locally finite graphs","volume":"39","author":"Halin","year":"1973"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB11","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0012-365X(88)90138-0","article-title":"A note on the growth of transitive graphs","volume":"73","author":"Imrich","year":"1988","journal-title":"Discrete Math."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB12","series-title":"Fundamentals of the Theory of Groups","author":"Kargapolov","year":"1979"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB13","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1112\/blms\/21.3.209","article-title":"A survey on spectra of infinite graphs","volume":"21","author":"Mohar","year":"1989","journal-title":"Bull. London Math. Soc."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB14","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1017\/S0013091500037640","article-title":"Harmonic functions and ends of graphs","volume":"31","author":"Picardello","year":"1988","journal-title":"Proc. Edinburgh Math. Soc."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB15","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/BF01304186","article-title":"Vertex transitive graphs","volume":"68","author":"Sabidussi","year":"1964","journal-title":"Monatsh. Math."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB16","doi-asserted-by":"crossref","unstructured":"P.M. Soardi and W. Woess, Amenability, unimodularity, and the spectral radius of random walks on infinite graphs, Math. Z., to appear.","DOI":"10.1007\/BF02571256"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB17","doi-asserted-by":"crossref","unstructured":"C. Thomassen, Resistance and currents in an infinite electrical network, J. Combin. Theory Ser. B, to appear.","DOI":"10.1016\/0095-8956(90)90065-8"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB18","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1070\/IM1984v022n02ABEH001449","article-title":"Automorphisms of graphs and a characterization of lattices","volume":"22","author":"Trofimov","year":"1984","journal-title":"Math. USSR-Izv."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB19","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1070\/SM1985v051n02ABEH002866","article-title":"Graphs with polynomial growth","volume":"51","author":"Trofimov","year":"1985","journal-title":"Math. USSR-Sb"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB20","first-page":"31","volume":"13","author":"Yamasaki","year":"1979"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB21","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/PROC.1976.10062","article-title":"Infinite electrical networks","volume":"64","author":"Zemanian","year":"1976","journal-title":"Proc. IEEE"},{"key":"10.1016\/0166-218X(91)90031-Q_BIB22","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1137\/0130029","article-title":"The complete behaviour of certain infinite networks under Kirchhoff's node and loop laws","volume":"30","author":"Zemanian","year":"1976","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/0166-218X(91)90031-Q_BIB23","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1137\/0512012","article-title":"The characteristic-resistance method for grounded semi-infinite grids","volume":"12","author":"Zemanian","year":"1981","journal-title":"SIAM J. Math. Anal."}],"container-title":["Discrete Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0166218X9190031Q?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0166218X9190031Q?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T05:58:29Z","timestamp":1555135109000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0166218X9190031Q"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,3]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,3]]}},"alternative-id":["0166218X9190031Q"],"URL":"https:\/\/doi.org\/10.1016\/0166-218x(91)90031-q","relation":{},"ISSN":["0166-218X"],"issn-type":[{"value":"0166-218X","type":"print"}],"subject":[],"published":{"date-parts":[[1991,3]]}}}