{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T04:09:22Z","timestamp":1754107762414,"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>We generalize a classical result of Sabidussi that was improved by Hemminger, to the case of directed color graphs.  The original results give a necessary and sufficient condition on two graphs, $C$ and $D$, for the automorphsim group of the wreath product of the graphs, ${\\rm Aut}(C\\wr D)$ to be the wreath product of the automorphism groups ${\\rm Aut}(C)\\wr {\\rm Aut}(D)$. Their characterization generalizes directly to the case of color graphs, but we show that there are additional exceptional cases in which either $C$ or $D$ is an infinite directed graph.  Also, we determine what ${\\rm Aut}(C \\wr D)$ is if ${\\rm Aut}(C \\wr D) \\neq {\\rm Aut} (C) \\wr {\\rm Aut} (D)$, and in particular, show that in this case there exist vertex-transitive graphs $C'$ and $D'$ such that $C' \\wr D' = C \\wr D$ and ${\\rm Aut} (C\\wr D) = {\\rm Aut} (C') \\wr {\\rm Aut}(D')$.<\/jats:p>","DOI":"10.37236\/106","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:36:14Z","timestamp":1578717374000},"source":"Crossref","is-referenced-by-count":8,"title":["Automorphism Groups of Wreath Product Digraphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Edward","family":"Dobson","sequence":"first","affiliation":[]},{"given":"Joy","family":"Morris","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,1,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:13:09Z","timestamp":1579317189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/106","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,1,30]]},"article-number":"R17"}}