{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T22:45:08Z","timestamp":1775083508675,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The domination polynomial $D(G,x)$ of a graph $G$ is the generating function\u00a0of its dominating sets. We prove that $D(G,x)$ satisfies a wide range of reduction formulas. We show linear recurrence relations for $D(G,x)$ for arbitrary graphs and for various special cases. We give splitting formulas for $D(G,x)$ based on articulation vertices, and more generally, on splitting sets of vertices. <\/jats:p>","DOI":"10.37236\/2475","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:23:29Z","timestamp":1578695009000},"source":"Crossref","is-referenced-by-count":24,"title":["Recurrence Relations and Splitting Formulas for the Domination Polynomial"],"prefix":"10.37236","volume":"19","author":[{"given":"Tomer","family":"Kotek","sequence":"first","affiliation":[]},{"given":"James","family":"Preen","sequence":"additional","affiliation":[]},{"given":"Frank","family":"Simon","sequence":"additional","affiliation":[]},{"given":"Peter","family":"Tittmann","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Trinks","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,10,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:29:06Z","timestamp":1579282146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i3p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,11]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/2475","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,11]]},"article-number":"P47"}}