{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:47Z","timestamp":1753893827928,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $H$ be a complex Hilbert space. Consider the ortho-Grassmann graph $\\Gamma^{\\perp}_{k}(H)$ whose vertices are $k$-dimensional subspaces of $H$ (projections of rank $k$) and two subspaces are connected by an edge in this graph if they are compatible and adjacent (the corresponding rank-$k$ projections commute and their difference is an operator of rank $2$). Our main result is the following: if $\\dim H\\ne 2k$, then every automorphism of $\\Gamma^{\\perp}_{k}(H)$ is induced by a unitary or anti-unitary operator; if $\\dim H=2k\\ge 6$, then every automorphism of $\\Gamma^{\\perp}_{k}(H)$ is induced by a unitary or anti-unitary operator or it is the composition of such an automorphism and the orthocomplementary map. For the case when $\\dim H=2k=4$ the statement fails. To prove this statement we compare geodesics of length two in ortho-Grassmann graphs and characterise compatibility (commutativity) in terms of geodesics in Grassmann and ortho-Grassmann graphs. At the end, we extend this result on generalised ortho-Grassmann graphs associated to conjugacy classes of finite-rank self-adjoint operators.<\/jats:p>","DOI":"10.37236\/10294","type":"journal-article","created":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T01:48:48Z","timestamp":1639705728000},"source":"Crossref","is-referenced-by-count":1,"title":["Automorphisms and Some Geodesic Properties of Ortho-Grassmann Graphs"],"prefix":"10.37236","volume":"28","author":[{"given":"Mark","family":"Pankov","sequence":"first","affiliation":[]},{"given":"Krzysztof","family":"Petelczyc","sequence":"additional","affiliation":[]},{"given":"Mariusz","family":"\u0179ynel","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,12,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T01:48:49Z","timestamp":1639705729000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i4p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,10,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10294","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,12,17]]},"article-number":"P4.49"}}