{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T02:18:33Z","timestamp":1775355513121,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A graph is minimally $k$-connected ($k$-edge-connected) if it is $k$-connected ($k$-edge-connected) and deleting any arbitrary chosen edge always leaves a graph which is not $k$-connected ($k$-edge-connected). Let $m= \\binom{d}{2}+t$, $1\\leq t\\leq d$ and $G_m$ be the graph obtained from the complete graph $K_d$ by adding one new vertex of degree $t$. Let $H_m$ be the graph obtained from $K_d\\backslash\\{e\\}$ by adding one new vertex adjacent to precisely two vertices of degree $d-1$ in $K_d\\backslash\\{e\\}$. Rowlinson [Linear Algebra Appl., 110 (1988) 43--53.] showed that $G_m$ attains the maximum spectral radius among all graphs of size $m$. This classic result indicates that $G_m$ attains the maximum spectral radius among all $2$-(edge)-connected graphs of size $m=\\binom{d}{2}+t$ except $t=1$. The next year, Rowlinson [Europ. J. Combin., 10 (1989) 489--497] proved that $H_m$ attains the maximum spectral radius among all $2$-connected graphs of size $m=\\binom{d}{2}+1$ ($d\\geq 5$), this also indicates $H_m$ is the unique extremal graph among all $2$-connected graphs of size $m=\\binom{d}{2}+1$ ($d\\geq 5$). Observe that neither $G_m$ nor $H_m$ are minimally $2$-(edge)-connected graphs. In this paper, we determine the maximum spectral radius for the minimally $2$-connected ($2$-edge-connected) graphs of given size; moreover, the corresponding extremal graphs are also characterized.<\/jats:p>","DOI":"10.37236\/11219","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T07:10:48Z","timestamp":1683270648000},"source":"Crossref","is-referenced-by-count":6,"title":["On the Spectral Radius of Minimally 2-(Edge)-Connected Graphs with Given Size"],"prefix":"10.37236","volume":"30","author":[{"given":"Zhenzhen","family":"Lou","sequence":"first","affiliation":[]},{"given":"Gao","family":"Min","sequence":"additional","affiliation":[]},{"given":"Qiongxiang","family":"Huang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,5,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T07:10:48Z","timestamp":1683270648000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i2p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/11219","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,5]]},"article-number":"P2.23"}}