{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:05:10Z","timestamp":1740107110605,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,3,14]],"date-time":"2022-03-14T00:00:00Z","timestamp":1647216000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,14]],"date-time":"2022-03-14T00:00:00Z","timestamp":1647216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571315"],"award-info":[{"award-number":["11571315"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s00373-022-02461-7","type":"journal-article","created":{"date-parts":[[2022,3,14]],"date-time":"2022-03-14T16:05:32Z","timestamp":1647273932000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Bipartite Graphs Having Minimum Fourth Adjacency Coefficient"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0635-8308","authenticated-orcid":false,"given":"Shi-Cai","family":"Gong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li-Ping","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shao-Wei","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,14]]},"reference":[{"key":"2461_CR1","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.21136\/CMJ.2020.0182-19","volume":"70","author":"M Andeli\u0107","year":"2020","unstructured":"Andeli\u0107, M., Du, Z., da Fonseca, C.M., Simi\u0107, S.K.: Tridiagonal matrices and spectral properties of some graph classes. J. Czech. Math. 70, 1125\u20131138 (2020)","journal-title":"J. Czech. Math."},{"issue":"10","key":"2461_CR2","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.laa.2010.12.017","volume":"435","author":"M Andeli\u0107","year":"2011","unstructured":"Andeli\u0107, M., da Fonseca, C.M., Simi\u0107, S.K., To\u0161i\u0107, D.V.: On bounds for the index of double nested graphs. Linear Algebra Appl. 435(10), 193\u2013210 (2011)","journal-title":"Linear Algebra Appl."},{"key":"2461_CR3","volume-title":"The Theory of Partitions","author":"G Andrews","year":"1976","unstructured":"Andrews, G.: The Theory of Partitions. Addison-Wesley Publishing Company, Boston (1976)"},{"key":"2461_CR4","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1016\/j.disc.2005.02.016","volume":"297","author":"Y Ashkenazi","year":"2005","unstructured":"Ashkenazi, Y.: $C_3$ saturated graphs. Discrete Math. 297, 152\u2013158 (2005)","journal-title":"Discrete Math."},{"key":"2461_CR5","doi-asserted-by":"publisher","first-page":"2168","DOI":"10.1016\/j.laa.2008.06.018","volume":"429","author":"FK Bell","year":"2008","unstructured":"Bell, F.K., Cvetkovi\u0107, D., Rowlinson, P., Simi\u0107, S.K.: Graphs for which the least eigenvalue is minimal, II. Linear Algebra Appl. 429, 2168\u20132179 (2008)","journal-title":"Linear Algebra Appl."},{"key":"2461_CR6","volume-title":"Algebraic Graph Theory","author":"NL Biggs","year":"1993","unstructured":"Biggs, N.L.: Algebraic Graph Theory. Cambridge University Press, Cambridge (1993)"},{"key":"2461_CR7","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/0095-8956(76)90057-5","volume":"21","author":"B Bollob\u00e1s","year":"1976","unstructured":"Bollob\u00e1s, B., Erd\u00f6s, P.: On a Ramsey\u2013Tur\u00e1n type problem. J. Combin. Theory B 21, 166\u2013168 (1976)","journal-title":"J. Combin. Theory B"},{"key":"2461_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325708","volume-title":"Combinatorial Matrix Theory","author":"RA Brualdi","year":"1991","unstructured":"Brualdi, R.A., Ryser, H.J.: Combinatorial Matrix Theory. Cambridge University Press, Cambridge (1991)"},{"key":"2461_CR9","volume-title":"Spectra of Graphs","author":"D Cvetkovi\u0107","year":"1980","unstructured":"Cvetkovi\u0107, D., Doob, M., Sachs, H.: Spectra of Graphs. Academic Press, New York (1980)"},{"key":"2461_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801518","volume-title":"An Introduction to the Theory of Graph Spectra","author":"D Cvetkovi\u0107","year":"2009","unstructured":"Cvetkovi\u0107, D., Rowlinson, P., Simi\u0107, S.: An Introduction to the Theory of Graph Spectra. Cambridge University Press, Cambridge (2009)"},{"key":"2461_CR11","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/0378-3758(93)90038-8","volume":"34","author":"IM Gessel","year":"1993","unstructured":"Gessel, I.M.: Counting paths in Young\u2019s lattice. J. Stat. Plan. Inference 34, 125\u2013134 (1993)","journal-title":"J. Stat. Plan. Inference"},{"key":"2461_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic Graph Theory","author":"C Godsil","year":"2001","unstructured":"Godsil, C., Royle, G.: Algebraic Graph Theory. Springer, New York (2001)"},{"key":"2461_CR13","doi-asserted-by":"publisher","first-page":"1934","DOI":"10.1080\/03081087.2016.1201082","volume":"65","author":"SC Gong","year":"2017","unstructured":"Gong, S.C.: On the rank of a real skew symmetric matrix described by an oriented graph. Linear Multilinear Algebra 65, 1934\u20131946 (2017)","journal-title":"Linear Multilinear Algebra"},{"key":"2461_CR14","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1002\/hlca.19560390623","volume":"39","author":"HH G\u00fcnthard","year":"1956","unstructured":"G\u00fcnthard, H.H., Primas, H.: Zusammenhang von Graphtheorie und Mo-Theotie von Molekeln mit Systemen konjugierter Bindungen. Helv. Chim. Acta 39, 1645\u20131653 (1956)","journal-title":"Helv. Chim. Acta"},{"key":"2461_CR15","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/0166-218X(90)90092-Q","volume":"28","author":"PL Hammer","year":"1990","unstructured":"Hammer, P.L., Peled, U.N., Sun, X.R.: Difference graphs. Discrete Appl. Math. 28, 35\u201344 (1990)","journal-title":"Discrete Appl. Math."},{"key":"2461_CR16","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1002\/jgt.3190100209","volume":"10","author":"L K\u00e1szonyi","year":"1986","unstructured":"K\u00e1szonyi, L., Tuza, Z.: Saturated graphs with minimal number of edges. J. Graph Theory 10, 203\u2013210 (1986)","journal-title":"J. Graph Theory"},{"issue":"6","key":"2461_CR17","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1007\/s00493-014-3188-y","volume":"36","author":"L Keough","year":"2016","unstructured":"Keough, L., Radcliffe, A.J.: Graphs with the fewest matchings. Combinatorica 36(6), 703\u2013723 (2016)","journal-title":"Combinatorica"},{"key":"2461_CR18","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.laa.2018.09.033","volume":"560","author":"J Lazzarin","year":"2019","unstructured":"Lazzarin, J., M\u00e1rquez, O.F., Tura, F.C.: No threshold graphs are cospectral. Linear Algebra Appl. 560, 133\u2013145 (2019)","journal-title":"Linear Algebra Appl."},{"key":"2461_CR19","doi-asserted-by":"publisher","first-page":"102164","DOI":"10.1016\/j.aam.2021.102164","volume":"127","author":"SC Li","year":"2021","unstructured":"Li, S.C., Yu, Y.T.: On a poset of trees revisited. Adv. Appl. Math. 127, 102164 (2021)","journal-title":"Adv. Appl. Math."},{"key":"2461_CR20","volume-title":"Threshold Graphs and Related Topics","author":"NVR Mahadev","year":"1995","unstructured":"Mahadev, N.V.R., Peled, U.N.: Threshold Graphs and Related Topics. Elsevier Publishers, Amsterdam (1995)"},{"key":"2461_CR21","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/0095-8956(72)90023-8","volume":"12","author":"A Mowshowitz","year":"1972","unstructured":"Mowshowitz, A.: The characteristic polynomial of a graph. J. Combin. Theory Ser. B 12, 177\u2013193 (1972)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2461_CR22","unstructured":"Schwenk, A.J., Wilson, R.J.: On the Eigenvalues of a Graph. Selected Topics in Graph Theory. Academic Press, New York (1978)"},{"key":"2461_CR23","first-page":"204","volume":"41","author":"YS Yang","year":"1992","unstructured":"Yang, Y.S., Rowlinson, P.: On extremal graphs without four-cycles. Util. Math. 41, 204\u2013220 (1992)","journal-title":"Util. Math."},{"key":"2461_CR24","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1137\/0603036","volume":"3","author":"M Yannakakis","year":"1982","unstructured":"Yannakakis, M.: The complexity of the partial order dimension problem. SIAM J. Algebr. Discrete Methods 3, 351\u2013358 (1982)","journal-title":"SIAM J. Algebr. Discrete Methods"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-022-02461-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-022-02461-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-022-02461-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T22:42:39Z","timestamp":1654814559000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-022-02461-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,14]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["2461"],"URL":"https:\/\/doi.org\/10.1007\/s00373-022-02461-7","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2022,3,14]]},"assertion":[{"value":"19 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 January 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 March 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have not disclosed any competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"60"}}