{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T19:01:31Z","timestamp":1773514891928,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,9,16]],"date-time":"2020-09-16T00:00:00Z","timestamp":1600214400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,16]],"date-time":"2020-09-16T00:00:00Z","timestamp":1600214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s00034-020-01541-4","type":"journal-article","created":{"date-parts":[[2020,9,16]],"date-time":"2020-09-16T06:02:36Z","timestamp":1600236156000},"page":"1511-1524","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some Two-Vertex Resistances of Nested Triangle Network"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7146-5639","authenticated-orcid":false,"given":"Muhammad Shoaib","family":"Sardar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5301-8739","authenticated-orcid":false,"given":"Xiang-Feng","family":"Pan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Si-Ao","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,9,16]]},"reference":[{"key":"1541_CR1","volume-title":"Modern Graph Theory, Volume 184 of Graduate Texts in Mathematics","author":"B Bollob\u00e1s","year":"1998","unstructured":"B. Bollob\u00e1s, Modern Graph Theory, Volume 184 of Graduate Texts in Mathematics (Springer, Berlin, 1998)"},{"key":"1541_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/qua.560500102","volume":"50","author":"D Bonchev","year":"1994","unstructured":"D. Bonchev, A.T. Balaban et al., Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances. Int. J. Quantum Chem. 50, 1\u201320 (1994)","journal-title":"Int. J. Quantum Chem."},{"key":"1541_CR3","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/0925-7721(94)00014-X","volume":"4","author":"G Battista","year":"1994","unstructured":"G. Battista, P. Di Eades et al., Algorithms for drawing graphs: an annotated bibliography. Comput. Geom. 4, 235\u2013282 (1994)","journal-title":"Comput. Geom."},{"key":"1541_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s13226-010-0004-2","volume":"41","author":"RB Bapat","year":"2010","unstructured":"R.B. Bapat, S. Gupta, Resistance distance in wheels and fans. Indian J. Pure Appl. Math. 41, 1\u201313 (2010)","journal-title":"Indian J. Pure Appl. Math."},{"key":"1541_CR5","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1016\/j.dam.2006.09.008","volume":"155","author":"H Chen","year":"2007","unstructured":"H. Chen, F. Zhang, Resistance distance and the normalized Laplacian spectrum. Discrete Appl. Math. 155, 654\u2013661 (2007)","journal-title":"Discrete Appl. Math."},{"key":"1541_CR6","doi-asserted-by":"publisher","DOI":"10.5948\/UPO9781614440222","volume-title":"Random Walks and Electric Networks","author":"PG Doyle","year":"1984","unstructured":"P.G. Doyle, J.L. Snell, Random Walks and Electric Networks (The Mathematical Association of America, Washington, DC, 1984)"},{"key":"1541_CR7","first-page":"401","volume":"75","author":"PW Fowler","year":"2002","unstructured":"P.W. Fowler, Resistance distances in Fullerene graphs. Croat. Chem. Acta 75, 401\u2013408 (2002)","journal-title":"Croat. Chem. Acta"},{"key":"1541_CR8","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.amc.2018.02.025","volume":"330","author":"J Fei","year":"2018","unstructured":"J. Fei, J. Tu, Complete characterization of bicyclic graphs with the maximum and second-maximum degree Kirchhoff index. Appl. Math. Comput. 330, 118\u2013124 (2018)","journal-title":"Appl. Math. Comput."},{"key":"1541_CR9","doi-asserted-by":"publisher","first-page":"2050","DOI":"10.1016\/j.dam.2011.06.027","volume":"17","author":"X Gao","year":"2011","unstructured":"X. Gao, Y. Luo, W. Liu, Resistance distances and the Kirchhoff index in Cayley graphs. Discrete Appl. Math. 17, 2050\u20132057 (2011)","journal-title":"Discrete Appl. Math."},{"key":"1541_CR10","doi-asserted-by":"publisher","first-page":"982","DOI":"10.1021\/ci960007t","volume":"36","author":"I Gutman","year":"1996","unstructured":"I. Gutman, B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide. J. Chem. Inf. Comput. Sci. 36, 982\u2013985 (1996)","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"1541_CR11","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s10955-009-9909-8","volume":"1","author":"S Jafarizadeh","year":"2010","unstructured":"S. Jafarizadeh, R. Sufiani, M.A. Jafarizadeh, Evaluation of effective resistances in pseudo-distance-regular resistor networks. J. Stat. Phys. 1, 177\u2013199 (2010)","journal-title":"J. Stat. Phys."},{"key":"1541_CR12","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.physa.2017.04.158","volume":"484","author":"Z Jiang","year":"2017","unstructured":"Z. Jiang, W. Yan, Resistance between two nodes of a ring network. Phys. A. 484, 21\u201326 (2017)","journal-title":"Phys. A."},{"key":"1541_CR13","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1007\/s10955-018-2067-0","volume":"172","author":"Z Jiang","year":"2018","unstructured":"Z. Jiang, W. Yan, Some two-point resistance of the Sierpinski gasket network. J. Stat. Phys. 172, 824\u2013832 (2018)","journal-title":"J. Stat. Phys."},{"key":"1541_CR14","first-page":"413","volume":"34","author":"AE Kennelly","year":"1899","unstructured":"A.E. Kennelly, Equivalence of triangles and stars in conducting networks. Electr. World Eng. 34, 413\u2013414 (1899)","journal-title":"Electr. World Eng."},{"key":"1541_CR15","first-page":"7","volume":"35","author":"DJ Klein","year":"1997","unstructured":"D.J. Klein, Graph geometry, graph metrics and Wiener. MATCH Commun. Math. Comput. Chem. 35, 7\u201327 (1997)","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"1541_CR16","first-page":"633","volume":"75","author":"DJ Klein","year":"2002","unstructured":"D.J. Klein, Resistance-distance sum rules. Croat. Chem. Acta 75, 633\u2013649 (2002)","journal-title":"Croat. Chem. Acta"},{"key":"1541_CR17","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1021\/ci00023a007","volume":"35","author":"DJ Klein","year":"1995","unstructured":"D.J. Klein, I. Lukovits, I. Gutman, On the definition of the hyper-wiener index for cycle-containing structures. J. Chem. Inf. Comput. Sci. 35, 50\u201352 (1995)","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"1541_CR18","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/BF01164627","volume":"12","author":"DJ Klein","year":"1993","unstructured":"D.J. Klein, M. Randi\u0107, Resistance distance. J. Math. Chem. 12, 81\u201395 (1993)","journal-title":"J. Math. Chem."},{"key":"1541_CR19","first-page":"306","volume":"3","author":"I Lukovits","year":"1999","unstructured":"I. Lukovits, S. Nikoli\u0107, N. Trinajsti\u0107, Resistance distance in regular graphs. Int. J. Quantum Chem. 3, 306\u2013313 (1999)","journal-title":"Int. J. Quantum Chem."},{"key":"1541_CR20","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.amc.2016.06.017","volume":"291","author":"JB Liu","year":"2016","unstructured":"J.B. Liu, X.F. Pan, Minimizing Kirchhoff index among graphs with a given vertex bipartiteness. Appl. Math. Comput. 291, 84\u201388 (2016)","journal-title":"Appl. Math. Comput."},{"key":"1541_CR21","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/S0024-3795(97)10080-5","volume":"278","author":"R Merris","year":"1998","unstructured":"R. Merris, Laplacian graph eigenvectors. Linear Algebra Appl. 278, 221\u2013236 (1998)","journal-title":"Linear Algebra Appl."},{"key":"1541_CR22","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.amc.2019.02.052","volume":"355","author":"X Ma","year":"2019","unstructured":"X. Ma, H. Bian, The normalized Laplacians, degree-Kirchhoff index and the spanning trees of hexagonal M$${\\ddot{o}}$$bius graphs. Appl. Math. Comput. 355, 33\u201346 (2019)","journal-title":"Appl. Math. Comput."},{"key":"1541_CR23","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1017\/S0305004100033879","volume":"55","author":"CSJA Nash-Williams","year":"1959","unstructured":"C.S.J.A. Nash-Williams, Random walks and electric currents in networks. Proc. Camb. Phil. Soc. 55, 181\u2013194 (1959)","journal-title":"Proc. Camb. Phil. Soc."},{"key":"1541_CR24","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1137\/0611030","volume":"11","author":"A Pothen","year":"1990","unstructured":"A. Pothen, H.D. Simon, K.P. Liou, Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11, 430\u2013452 (1990)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1541_CR25","first-page":"916","volume":"62","author":"A Rosen","year":"1924","unstructured":"A. Rosen, A new network theorem. J. Inst. Electr. Eng. 62, 916\u2013918 (1924)","journal-title":"J. Inst. Electr. Eng."},{"key":"1541_CR26","volume-title":"Generalized Inverse of Matrices and Its Applications","author":"CR Rao","year":"1971","unstructured":"C.R. Rao, S.K. Mitra, Generalized Inverse of Matrices and Its Applications (Wiley, New York, 1971)"},{"key":"1541_CR27","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.dam.2015.09.017","volume":"203","author":"VG Severino","year":"2016","unstructured":"V.G. Severino, Resistance distance in complete $$n$$- partite graphs. Discrete Appl. Math. 203, 53\u201361 (2016)","journal-title":"Discrete Appl. Math."},{"key":"1541_CR28","doi-asserted-by":"publisher","first-page":"120782","DOI":"10.1016\/j.physa.2019.04.018","volume":"526","author":"MS Sardar","year":"2019","unstructured":"M.S. Sardar, H. Hua, X.F. Pan, H. Raza, On the resistance diameter of hypercubes. Phys. A. 526, 120782 (2019)","journal-title":"Phys. A."},{"key":"1541_CR29","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1007\/s10955-020-02569-1","volume":"181","author":"MS Sardar","year":"2020","unstructured":"M.S. Sardar, X.F. Pan, Y.X. Li, Some two-vertex resistances of the three-towers Hanoi graph formed by a fractal graph. J. Stat. Phys. 181, 116\u2013131 (2020)","journal-title":"J. Stat. Phys."},{"key":"1541_CR30","doi-asserted-by":"crossref","first-page":"125283","DOI":"10.1016\/j.amc.2020.125283","volume":"381","author":"MS Sardar","year":"2020","unstructured":"M.S. Sardar, X.F. Pan, S.A. Xu, Computation of Resistance distance and Kirchhoff index of the two classes of silicate networks. Appl. Math. Comput. 381, 125283 (2020)","journal-title":"Appl. Math. Comput."},{"key":"1541_CR31","volume-title":"Linear Graphs and Electrical Networks","author":"S Seshu","year":"1961","unstructured":"S. Seshu, M.B. Reed, Linear Graphs and Electrical Networks (Addison-Wesley, Reading, Mass, 1961)"},{"key":"1541_CR32","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1109\/TCT.1960.1086671","volume":"7","author":"GE Sharpe","year":"1960","unstructured":"G.E. Sharpe, B. Spain, On the solution of networks by means of the equicofactor matrix. IRE Trans. Circuit Theory 7, 230\u2013239 (1960)","journal-title":"IRE Trans. Circuit Theory"},{"key":"1541_CR33","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1109\/TCT.1965.1082367","volume":"12","author":"GE Sharpe","year":"1965","unstructured":"G.E. Sharpe, G.P.H. Styan, Circuit duality and the general network inverse. IEEE Trans. Circuit Theory 12, 22\u201327 (1965)","journal-title":"IEEE Trans. Circuit Theory"},{"key":"1541_CR34","doi-asserted-by":"publisher","first-page":"1226","DOI":"10.1109\/PROC.1967.5805","volume":"55","author":"GE Sharpe","year":"1967","unstructured":"G.E. Sharpe, G.P.H. Styan, A note on equicofactor matrices. Proc. IEEE. 55, 1226\u20131227 (1967)","journal-title":"Proc. IEEE."},{"key":"1541_CR35","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1109\/CEEJ.1983.6591843","volume":"8","author":"MNS Swamy","year":"1983","unstructured":"M.N.S. Swamy, K. Thulasiraman, A theorem in the theory of determinants and the number of spanning trees of a graph. Can. Elect. Eng. J. 8, 147\u2013152 (1983)","journal-title":"Can. Elect. Eng. J."},{"key":"1541_CR36","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1016\/j.amc.2015.06.063","volume":"268","author":"J Tu","year":"2015","unstructured":"J. Tu, J. Du, G. Su, The unicyclic graphs with maximum degree resistance distance. Appl. Math. Comput. 268, 859\u2013864 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1541_CR37","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1021\/ci950116s","volume":"36","author":"HY Zhu","year":"1996","unstructured":"H.Y. Zhu, D.J. Klein, I. Lukovits, Extensions of the Wiener number. J. Chem. Inf. Comput. Sci. 36, 420\u2013428 (1996)","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"1541_CR38","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1002\/qua.21068","volume":"107","author":"HP Zhang","year":"2007","unstructured":"H.P. Zhang, Y.J. Yang, Resistance distance and Kirchhoff index in circulant graphs. Int. J. Quantum Chem. 107, 330\u2013339 (2007)","journal-title":"Int. J. Quantum Chem."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-020-01541-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-020-01541-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-020-01541-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T22:07:10Z","timestamp":1723586830000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-020-01541-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,16]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["1541"],"URL":"https:\/\/doi.org\/10.1007\/s00034-020-01541-4","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,16]]},"assertion":[{"value":"2 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 August 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 September 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 September 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}