{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:51Z","timestamp":1753893831061,"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>A 2-distance-primitive graph is a vertex-transitive graph whose vertex stabilizer is primitive on both the first step and the second step neighborhoods. Let $\\Gamma$ be such a graph. This paper shows that either $\\Gamma$ is a cyclic graph, or $\\Gamma$ is a complete bipartite graph, or $\\Gamma$ has girth at most $4$ and the vertex stabilizer acts faithfully on both the first step and the second step neighborhoods. Also a complete classification is given of such graphs\u00a0 satisfying that the vertex stabilizer acts $2$-transitively on the second step neighborhood. Finally, we determine the unique 2-distance-primitive graph which is\u00a0 locally cyclic.<\/jats:p>","DOI":"10.37236\/8890","type":"journal-article","created":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T01:44:37Z","timestamp":1608774277000},"source":"Crossref","is-referenced-by-count":0,"title":["Two-Distance-Primitive Graphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Wei","family":"Jin","sequence":"first","affiliation":[]},{"given":"Ci Xuan","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Jin Xin","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,12,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p53\/8234","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p53\/8234","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T01:44:37Z","timestamp":1608774277000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,24]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/8890","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,12,24]]},"article-number":"P4.53"}}