{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:24Z","timestamp":1753893864233,"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>Two graphs are said to be generalized cospectral\u00a0if they have the same characteristic polynomials and so do their complements. A graph is controllable\u00a0if its walk matrix is nonsingular; equivalently, if all the eigenvalues of its adjacency matrix are simple and main. A graph $H$ on $(n+1)$ vertices is an overgraph of another graph $G$ on $n$ vertices if $G$ is a vertex-deleted subgraph of $H$. We prove that no two distinct overgraphs of a controllable graph are generalized cospectral; this strengthens an earlier result that stated that no two such overgraphs are isomorphic. Moreover, we present methods that produce pairs of generalized cospectral graphs $G^\\prime$ and $H^\\prime$ starting from a pair of generalized cospectral, non-isomorphic, controllable graphs $G$ and $H$. We show that if $G^\\prime$ and $H^\\prime$ are controllable, then they are non-isomorphic.<\/jats:p>","DOI":"10.37236\/7883","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:16:10Z","timestamp":1578640570000},"source":"Crossref","is-referenced-by-count":0,"title":["The Overgraphs of Generalized Cospectral Controllable Graphs"],"prefix":"10.37236","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6562-0567","authenticated-orcid":false,"given":"Alexander","family":"Farrugia","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,1,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p14\/7772","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p14\/7772","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:18:46Z","timestamp":1579234726000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7883","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,1,25]]},"article-number":"P1.14"}}