{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:05Z","timestamp":1753893845297,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The algebraic connectivity of a graph $G$ is the second smallest eigenvalue of its Laplacian matrix. Let $\\mathscr{B}_n$ be the set of all bicyclic graphs of order $n$. In this paper, we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in $\\mathscr{B}_n$ when $n\\geq 13$. This result, together with our previous results on trees and unicyclic graphs, can be used to further determine the last sixteen graphs among all connected graphs of order $n$. This extends the results of Shao et al. [The ordering of trees and connected graphs by their algebraic connectivity, Linear Algebra Appl. 428 (2008) 1421-1438].<\/jats:p>","DOI":"10.37236\/434","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:59:04Z","timestamp":1578715144000},"source":"Crossref","is-referenced-by-count":4,"title":["The Orderings of Bicyclic Graphs and Connected Graphs by Algebraic Connectivity"],"prefix":"10.37236","volume":"17","author":[{"given":"Jianxi","family":"Li","sequence":"first","affiliation":[]},{"given":"Ji-Ming","family":"Guo","sequence":"additional","affiliation":[]},{"given":"Wai Chee","family":"Shiu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,12,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r162\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r162\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:21:36Z","timestamp":1579303296000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/434","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,12,3]]},"article-number":"R162"}}