{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T20:16:04Z","timestamp":1712348164806},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"A finite graph $\\Gamma$ is $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on $V(\\Gamma)$ and transitively on the set of ordered pairs of adjacent vertices of $\\Gamma$. If $V(\\Gamma)$ admits a nontrivial $G$-invariant partition ${\\cal B}$ such that for blocks $B, C \\in {\\cal B}$ adjacent in the quotient graph $\\Gamma_{{\\cal B}}$ relative to ${\\cal B}$, exactly one vertex of $B$ has no neighbour in $C$, then we say that $\\Gamma$ is an almost multicover of $\\Gamma_{{\\cal B}}$. In this case there arises a natural incidence structure ${\\cal D}(\\Gamma, {\\cal B})$ with point set ${\\cal B}$. If in addition $\\Gamma_{{\\cal B}}$ is a complete graph, then ${\\cal D}(\\Gamma, {\\cal B})$ is a $(G, 2)$-point-transitive and $G$-block-transitive $2$-$(|{\\cal B}|, m+1, \\lambda)$ design for some $m \\geq 1$, and moreover either $\\lambda=1$ or $\\lambda=m+1$. In this paper we classify such graphs in the case when $\\lambda = m+1$; this together with earlier classifications when $\\lambda = 1$ gives a complete classification of almost multicovers of complete graphs.<\/jats:p>","DOI":"10.37236\/5701","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:08:58Z","timestamp":1578690538000},"source":"Crossref","is-referenced-by-count":2,"title":["A Family of Symmetric Graphs with Complete Quotients"],"prefix":"10.37236","volume":"23","author":[{"given":"Teng","family":"Fang","sequence":"first","affiliation":[]},{"given":"Xin Gui","family":"Fang","sequence":"additional","affiliation":[]},{"given":"Binzhou","family":"Xia","sequence":"additional","affiliation":[]},{"given":"Sanming","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,5,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:28:28Z","timestamp":1579238908000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5701","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,13]]}}}