{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T22:10:02Z","timestamp":1740262202623,"version":"3.37.3"},"publisher-location":"Berlin, Heidelberg","reference-count":25,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540241317"},{"type":"electronic","value":"9783540305514"}],"license":[{"start":{"date-parts":[[2004,1,1]],"date-time":"2004-01-01T00:00:00Z","timestamp":1072915200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004]]},"DOI":"10.1007\/978-3-540-30551-4_45","type":"book-chapter","created":{"date-parts":[[2010,7,13]],"date-time":"2010-07-13T18:15:37Z","timestamp":1279044937000},"page":"508-521","source":"Crossref","is-referenced-by-count":4,"title":["Counting Spanning Trees and Other Structures in Non-constant-jump Circulant Graphs"],"prefix":"10.1007","author":[{"given":"Mordecai J.","family":"Golin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiu Cho","family":"Leung","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yajun","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"45_CR1","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1080\/00150517.1985.12429821","volume":"23.3","author":"G. Baron","year":"1985","unstructured":"Baron, G., Prodinger, H., Tichy, R.F., Boesch, F.T., Wang, J.F.: The Number of Spanning Trees in the Square of a Cycle. Fibonacci Quarterly\u00a023.3, 258\u2013264 (1985)","journal-title":"Fibonacci Quarterly"},{"key":"45_CR2","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/0016-0032(73)90227-5","volume":"295","author":"S. Bedrosian","year":"1973","unstructured":"Bedrosian, S.: The Fibonacci Numbers via Trigonometric Expressions. J. Franklin Inst.\u00a0295, 175\u2013177 (1973)","journal-title":"J. Franklin Inst."},{"key":"45_CR3","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1006\/jpdc.1995.1002","volume":"24","author":"J.-C. Bermond","year":"1995","unstructured":"Bermond, J.-C., Comellas, F., Hsu, D.F.: Distributed Loop Computer Networks: A Survey. Journal of Parallel and Distributed Computing\u00a024, 2\u201310 (1995)","journal-title":"Journal of Parallel and Distributed Computing"},{"key":"45_CR4","series-title":"Second Edition","volume-title":"Algebraic Graph Theory","author":"N. Biggs","year":"1993","unstructured":"Biggs, N.: Algebraic Graph Theory. Second Edition. Cambridge University Press, London (1993)"},{"key":"45_CR5","first-page":"16","volume-title":"Notes from New York Graph Theory Day","author":"F.T. Boesch","year":"1982","unstructured":"Boesch, F.T., Wang, J.F.: A Conjecture on the Number of Spanning Trees in the Square of a Cycle. In: Notes from New York Graph Theory Day, p. 16. New York Academy Sciences, New York (1982)"},{"key":"45_CR6","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/BF01788093","volume":"2","author":"F.T. Boesch","year":"1986","unstructured":"Boesch, F.T., Prodinger, H.: Spanning Tree Formulas and Chebyshev Polynomials. Graphs and Combinatorics\u00a02, 191\u2013200 (1986)","journal-title":"Graphs and Combinatorics"},{"key":"45_CR7","unstructured":"Brightwell, G.R., Winkler, P.: Note on Counting Eulerian Circuits. lanl.arXiv.org, cs.CC\/0405067 (May 19 2004)"},{"key":"45_CR8","volume-title":"The combinatorics of network reliability","author":"C.J. Colbourn","year":"1987","unstructured":"Colbourn, C.J.: The combinatorics of network reliability. Oxford University Press, New York (1987)"},{"key":"45_CR9","volume-title":"Spectra of Graphs: Theory and Applications, Third Edition","author":"D. Cvetkovi\u010d","year":"1995","unstructured":"Cvetkovi\u010d, D., Doob, M., Sachs, H.: Spectra of Graphs: Theory and Applications, Third Edition. Johann Ambrosius Barth, Heidelberg (1995)"},{"key":"45_CR10","first-page":"541","volume-title":"Mathematics and Computer Science II: Algorithms, Trees, Combinatorics and Probabilities","author":"M.J. Golin","year":"2002","unstructured":"Golin, M.J., Zhang, Y.P.: Further applications of Chebyshev polynomials in the derivation of spanning tree formulas for circulant graphs. In: Mathematics and Computer Science II: Algorithms, Trees, Combinatorics and Probabilities, pp. 541\u2013552. Birkhauser-Verlag, Basel (2002)"},{"key":"45_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1007\/978-3-540-30559-0_25","volume-title":"Graph-Theoretic Concepts in Computer Science","author":"M.J. Golin","year":"2004","unstructured":"Golin, M.J., Leung, Y.C.: Unhooking circulant graphs: A combinatorial method for counting spanning trees and other parameters. In: Hromkovi\u010d, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol.\u00a03353, pp. 296\u2013307. Springer, Heidelberg (2004)"},{"key":"45_CR12","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0304-3975(01)00341-3","volume":"299","author":"F.K. Hwang","year":"2003","unstructured":"Hwang, F.K.: A survey on multi-loop networks. Theoretical Computer Science\u00a0299, 107\u2013121 (2003)","journal-title":"Theoretical Computer Science"},{"key":"45_CR13","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1002\/andp.18471481202","volume":"72","author":"G. Kirchhoff","year":"1847","unstructured":"Kirchhoff, G.: \u201c\u00dcber die Aufl\u00f6sung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Str\u00f6me gef\u00fchrt wird,\u201d. Ann. Phys. Chem.\u00a072, 497\u2013508 (1847)","journal-title":"Ann. Phys. Chem."},{"key":"45_CR14","doi-asserted-by":"publisher","first-page":"40","DOI":"10.2307\/2319131","volume":"82","author":"D.J. Kleitman","year":"1975","unstructured":"Kleitman, D.J., Golden, B.: Counting Trees in a Certain Class of Graphs. Amer. Math. Monthly\u00a082, 40\u201344 (1975)","journal-title":"Amer. Math. Monthly"},{"key":"45_CR15","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/S0012-365X(97)00086-1","volume":"184","author":"J.P. McSorley","year":"1998","unstructured":"McSorley, J.P.: Counting structures in the M\u00f6bius ladder. Discrete Mathematics\u00a0184, 137\u2013164 (1998)","journal-title":"Discrete Mathematics"},{"key":"45_CR16","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1007\/BF01940872","volume":"16","author":"M. Mihail","year":"1996","unstructured":"Mihail, M., Winkler, P.: On the number of Eulerian orientations of a graph. Algorithmica\u00a016, 402\u2013414 (1996)","journal-title":"Algorithmica"},{"key":"45_CR17","unstructured":"Rubey, M.: Counting Spanning Trees, May 2000. Diplomarbeit, Universitat Wein (2000)"},{"key":"45_CR18","unstructured":"Sedlacek, J.: On the skeletons of a Graph or Digraph. In: Guy, R.K., et al. (eds.) Combinatorial Structures and their Applications, pp. 387\u2013391 (1970)"},{"key":"45_CR19","unstructured":"Sjogren, J.A.: Note on a formula of Kleitman and Golden on spanning trees in circulant graphs. In: Proceedings of the Twenty-second Southeastern Conference on Combinatorics, Graph Theory, and Computing, Congr. Numer., vol.\u00a083, pp. 65\u201373 (1991)"},{"key":"45_CR20","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1137\/0208032","volume":"8","author":"L.G. Valiant","year":"1979","unstructured":"Valiant, L.G.: The complexity of enumeration and reliability problems. SIAM J. Comput\u00a08, 410\u2013421 (1979)","journal-title":"SIAM J. Comput"},{"issue":"5","key":"45_CR21","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/0016-0032(84)90054-1","volume":"318","author":"R. Vohra","year":"1984","unstructured":"Vohra, R., Washington, L.: Counting spanning trees in the graphs of Kleitman and Golden and a generalization. J. Franklin Inst.\u00a0318(5), 349\u2013355 (1984)","journal-title":"J. Franklin Inst."},{"key":"45_CR22","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/S0012-365X(96)00298-1","volume":"176","author":"Q.F. Yang","year":"1997","unstructured":"Yang, Q.F., Burkard, R.E., Cela, E., Woeginger, G.: Hamiltonian cycles in circulant digraphs with two stripes. Discrete Math.\u00a0176, 233\u2013254 (1997)","journal-title":"Discrete Math."},{"key":"45_CR23","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/S0012-365X(96)00092-1","volume":"169","author":"X. Yong","year":"1997","unstructured":"Yong, X., Talip, Acenjian: The Numbers of Spanning Trees of the Cubic Cycle $C_N^3$ and the Quadruple Cycle $C_N^4$ . Discrete Math.\u00a0169, 293\u2013298 (1997)","journal-title":"Discrete Math."},{"key":"45_CR24","first-page":"12","volume":"11","author":"X. Yong","year":"1994","unstructured":"Yong, X., Zhang, F.J.: A simple proof for the complexity of square cycle C 2 p . J. Xinjiang Univ.\u00a011, 12\u201316 (1994)","journal-title":"J. Xinjiang Univ."},{"key":"45_CR25","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/S0012-365X(99)00414-8","volume":"223","author":"Y.P. Zhang","year":"2000","unstructured":"Zhang, Y.P., Yong, X., Golin, M.J.: The number of spanning trees in circulant graphs. Discrete Math\u00a0223, 337\u2013350 (2000)","journal-title":"Discrete Math"}],"container-title":["Lecture Notes in Computer Science","Algorithms and Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-30551-4_45","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T21:52:27Z","timestamp":1740261147000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-30551-4_45"}},"subtitle":["(Extended Abstract)"],"short-title":[],"issued":{"date-parts":[[2004]]},"ISBN":["9783540241317","9783540305514"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-30551-4_45","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2004]]}}}