{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:10Z","timestamp":1753893790120,"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>A differential poset is a partially ordered set with raising and lowering operators $U$ and $D$ which satisfy the commutation relation $DU-UD=rI$ for some constant $r$. This notion may be generalized to deal with the case in which there exist sequences of constants $\\{q_n\\}_{n\\geq 0}$ and $\\{r_n\\}_{n\\geq 0}$ such that for any poset element $x$ of rank $n$, $DU(x) = q_n UD(x) + r_nx$. Here, we introduce natural raising and lowering operators such that the set of unlabelled graphs, ordered by $G\\leq H$ if and only if $G$ is isomorphic to an induced subgraph of $H$, is a generalized differential poset with $q_n=2$ and $r_n = 2^n$. This allows one to apply a number of enumerative results regarding walk enumeration to the poset of induced subgraphs.<\/jats:p>","DOI":"10.37236\/1155","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:56:08Z","timestamp":1578718568000},"source":"Crossref","is-referenced-by-count":0,"title":["The Induced Subgraph Order on Unlabelled Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"Craig A.","family":"Sloss","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,10,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:07:06Z","timestamp":1579320426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1n17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1155","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,10,27]]},"article-number":"N17"}}