{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T23:30:12Z","timestamp":1773790212067,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is the graph obtained by joining a vertex to a path on $n-1$ vertices. In this paper, we disprove this conjecture by showing that the extremal graph is the graph obtained by joining a vertex to a path on $\\lceil(2n-1)\/3\\rceil$ vertices and $\\lfloor(n-2)\/3\\rfloor$ isolated vertices. For planar graphs, we show that the extremal $n$-vertex planar graph attaining the maximum spread is the graph obtained by joining two nonadjacent vertices to a path on $\\lceil(2n-2)\/3\\rceil$ vertices and $\\lfloor(n-4)\/3\\rfloor$ isolated vertices.<\/jats:p>","DOI":"10.37236\/11844","type":"journal-article","created":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T15:01:58Z","timestamp":1725548518000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Maximum Spread of Planar and Outerplanar Graphs"],"prefix":"10.37236","volume":"31","author":[{"given":"Zelong","family":"Li","sequence":"first","affiliation":[]},{"given":"William","family":"Linz","sequence":"additional","affiliation":[]},{"given":"Linyuan","family":"Lu","sequence":"additional","affiliation":[]},{"given":"Zhiyu","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2024,9,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T15:01:58Z","timestamp":1725548518000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i3p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,6]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/11844","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,6]]},"article-number":"P3.25"}}