{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:07:51Z","timestamp":1758823671881,"version":"3.37.3"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T00:00:00Z","timestamp":1619395200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T00:00:00Z","timestamp":1619395200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai","doi-asserted-by":"publisher","award":["Grant No. 12ZR1420300"],"award-info":[{"award-number":["Grant No. 12ZR1420300"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No.11101284","11201303"],"award-info":[{"award-number":["No.11101284","11201303"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11301340"],"award-info":[{"award-number":["11301340"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s40314-021-01498-3","type":"journal-article","created":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T16:31:08Z","timestamp":1619454668000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On the index of unbalanced signed bicyclic graphs"],"prefix":"10.1007","volume":"40","author":[{"given":"Changxiang","family":"He","sequence":"first","affiliation":[]},{"given":"Yuying","family":"Li","sequence":"additional","affiliation":[]},{"given":"Haiying","family":"Shan","sequence":"additional","affiliation":[]},{"given":"Wenyan","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,26]]},"reference":[{"key":"1498_CR1","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.laa.2019.06.016","volume":"581","author":"S Akbari","year":"2019","unstructured":"Akbari S, Belardo F, Heydari F, Maghasedi M, Souri M (2019) On the largest eigenvalue of signed unicyclic graphs. Linear Algebra Appl 581:145\u2013162","journal-title":"Linear Algebra Appl"},{"key":"1498_CR2","doi-asserted-by":"publisher","first-page":"1513","DOI":"10.1016\/j.laa.2010.05.010","volume":"433","author":"F Belardo","year":"2010","unstructured":"Belardo F, Li Marzi EM, Simic SK (2010) Combinatorial approach for computing the characteristic polynomial of a matrix. Linear Algebra Appl 433:1513\u20131523","journal-title":"Linear Algebra Appl"},{"key":"1498_CR3","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.laa.2018.07.026","volume":"557","author":"F Belardo","year":"2018","unstructured":"Belardo F, Brunetti M, Ciampella A (2018) Signed bicyclic graphs minimizing the least Laplacian eigenvalue. Linear Algebra Appl 557:201\u2013233","journal-title":"Linear Algebra Appl"},{"key":"1498_CR4","doi-asserted-by":"publisher","DOI":"10.21136\/CMJ.2020.0403-19","author":"F Belardo","year":"2020","unstructured":"Belardo F, Brunetti M, Ciampella A (2020) Unbalanced unicyclic and bicyclic graphs with extremal spectral radius. Czech Math J. https:\/\/doi.org\/10.21136\/CMJ.2020.0403-19 (in press)","journal-title":"Czech Math J"},{"key":"1498_CR5","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.dam.2017.03.015","volume":"226","author":"MA Bhat","year":"2017","unstructured":"Bhat MA, Pirzada S (2017) Unicyclic signed graphs with minimal energy. Discret Appl Math 226:32\u201339","journal-title":"Discret Appl Math"},{"key":"1498_CR6","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.laa.2018.03.047","volume":"551","author":"MA Bhat","year":"2018","unstructured":"Bhat MA, Samee U, Pirzada S (2018) Bicyclic signed graphs with minimal and second minimal energy. Linear Algebra Appl 551:18\u201335","journal-title":"Linear Algebra Appl"},{"key":"1498_CR7","volume-title":"An introduction to the theory of graph spectra","author":"DM Cvetkovic","year":"2010","unstructured":"Cvetkovic DM, Rowlinson P, Simic SK (2010) An introduction to the theory of graph spectra. Cambridge University Press, Cambridge"},{"key":"1498_CR8","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1016\/j.laa.2012.08.027","volume":"438","author":"Y Fan","year":"2013","unstructured":"Fan Y, Wang Y, Wang Y (2013) A note on the nullity of unicyclic signed graphs. Linear Algebra Appl 438:1193\u20131200","journal-title":"Linear Algebra Appl"},{"key":"1498_CR9","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1016\/j.amc.2018.11.040","volume":"347","author":"S Hafeeza","year":"2019","unstructured":"Hafeeza S, Farooq R, Khan M (2019) Bicyclic signed digraphs with maximal energy. Appl Math Comput 347:702\u2013711","journal-title":"Appl Math Comput"},{"key":"1498_CR10","doi-asserted-by":"publisher","first-page":"3404","DOI":"10.1016\/j.disc.2010.08.012","volume":"310","author":"CX He","year":"2010","unstructured":"He CX, Shan HY (2010) On the Laplacian coefficients of bicyclic graphs. Discret Math 310:3404\u20133412","journal-title":"Discret Math"},{"key":"1498_CR11","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.dam.2013.12.018","volume":"169","author":"S Pirzada","year":"2014","unstructured":"Pirzada S, Bhat Mushtaq A (2014) Energy of signed digraphs. Discret Appl Math 169:195\u2013205","journal-title":"Discret Appl Math"},{"key":"1498_CR12","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/S1571-0653(04)00017-4","volume":"2","author":"FS Roberts","year":"1999","unstructured":"Roberts FS (1999) On balanced signed graphs and consistent marked graphs. Electron Notes Discret Math 2:94\u2013105","journal-title":"Electron Notes Discret Math"},{"key":"1498_CR13","doi-asserted-by":"publisher","first-page":"841","DOI":"10.7151\/dmgt.2035","volume":"38","author":"Z Stanic","year":"2018","unstructured":"Stanic Z (2018) Pertubations in a signed graph and its index. Discuss Math Graph Theory 38:841\u2013852","journal-title":"Discuss Math Graph Theory"},{"key":"1498_CR14","unstructured":"Wang D, Hou Y (2018) Unicyclic signed graphs with maximal energy. arXiv:1809.06206"},{"key":"1498_CR15","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1016\/j.dam.2019.01.034","volume":"260","author":"D Wang","year":"2019","unstructured":"Wang D, Hou Y (2019) Bicyclic signed graphs with at most one odd cycle and maximal energy. Discret Appl Math 260:244\u2013255","journal-title":"Discret Appl Math"},{"key":"1498_CR16","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/0166-218X(82)90033-6","volume":"4","author":"T Zaslavsky","year":"1982","unstructured":"Zaslavsky T (1982) Signed graphs. Discret Appl Math 4:47\u201374","journal-title":"Discret Appl Math"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01498-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01498-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01498-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T19:37:07Z","timestamp":1698953827000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01498-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,26]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1498"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01498-3","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,4,26]]},"assertion":[{"value":"8 December 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"124"}}