{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:52:30Z","timestamp":1753894350348,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2023,2,4]],"date-time":"2023-02-04T00:00:00Z","timestamp":1675468800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper, we study geodesic growth of numbered graph products; these are\na generalization of right-angled Coxeter groups, defined as graph products of\nfinite cyclic groups. We first define a graph-theoretic condition called\nlink-regularity, as well as a natural equivalence amongst link-regular numbered\ngraphs, and show that numbered graph products associated to link-regular\nnumbered graphs must have the same geodesic growth series. Next, we derive a\nformula for the geodesic growth of right-angled Coxeter groups associated to\nlink-regular graphs. Finally, we find a system of equations that can be used to\nsolve for the geodesic growth of numbered graph products corresponding to\nlink-regular numbered graphs that contain no triangles and have constant vertex\nnumbering.<\/jats:p>","DOI":"10.46298\/jgcc.2023.14.2.10019","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T08:34:37Z","timestamp":1675672477000},"source":"Crossref","is-referenced-by-count":0,"title":["Geodesic Growth of Numbered Graph Products"],"prefix":"10.46298","volume":"Volume 14, Issue 2","author":[{"given":"Lindsay","family":"Marjanski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Solon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kathleen","family":"Zopff","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2023,2,4]]},"container-title":["journal of Groups, complexity, cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/gcc.episciences.org\/10850\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/gcc.episciences.org\/10850\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T10:13:01Z","timestamp":1687255981000},"score":1,"resource":{"primary":{"URL":"https:\/\/gcc.episciences.org\/10019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,4]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/jgcc.2023.14.2.10019","relation":{"has-preprint":[{"id-type":"arxiv","id":"2208.13095v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2208.13095","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2208.13095","asserted-by":"subject"}]},"ISSN":["1869-6104"],"issn-type":[{"type":"electronic","value":"1869-6104"}],"subject":[],"published":{"date-parts":[[2023,2,4]]},"article-number":"10019"}}