{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T17:07:22Z","timestamp":1776186442358,"version":"3.50.1"},"reference-count":4,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,5,5]],"date-time":"2009-05-05T00:00:00Z","timestamp":1241481600000},"content-version":"vor","delay-in-days":124,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004530","name":"University Putra Malaysia","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004530","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>Let <jats:italic>G<\/jats:italic> = (<jats:italic>V<\/jats:italic>, <jats:italic>E<\/jats:italic>) be a simple graph. A set <jats:italic>S<\/jats:italic>\u2286<jats:italic>V<\/jats:italic> is a dominating set of <jats:italic>G<\/jats:italic>, if every vertex in <jats:italic>V<\/jats:italic>\\<jats:italic>S<\/jats:italic> is adjacent to at least one vertex in <jats:italic>S<\/jats:italic>. Let  be the family of all dominating sets of a path <jats:italic>P<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> with cardinality <jats:italic>i<\/jats:italic>, and let . In this paper, we construct , and obtain a recursive formula for <jats:italic>d<\/jats:italic>(<jats:italic>P<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, <jats:italic>i<\/jats:italic>). Using this recursive formula, we consider the polynomial , which we call domination polynomial of paths and obtain some properties of this polynomial.<\/jats:p>","DOI":"10.1155\/2009\/542040","type":"journal-article","created":{"date-parts":[[2009,5,5]],"date-time":"2009-05-05T13:52:02Z","timestamp":1241531522000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Dominating Sets and Domination Polynomials of Paths"],"prefix":"10.1155","volume":"2009","author":[{"given":"Saeid","family":"Alikhani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yee-Hock","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2009,5,5]]},"reference":[{"key":"e_1_2_5_1_2","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"e_1_2_5_2_2","series-title":"Series of Books in the Mathematical Science","volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","author":"Garey M. R.","year":"1979"},{"key":"e_1_2_5_3_2","unstructured":"AlikhaniS.andPengY. H. Introduction to domination polynomial of a graph to appear inArs Combinatoria."},{"key":"e_1_2_5_4_2","volume-title":"Introduction to Graph Theory","author":"Chartrand G.","year":"2005"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2009\/542040.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2009\/542040.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2009\/542040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T15:00:19Z","timestamp":1719068419000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2009\/542040"}},"subtitle":[],"editor":[{"given":"Alexander","family":"Rosa","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1155\/2009\/542040"],"URL":"https:\/\/doi.org\/10.1155\/2009\/542040","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]},"assertion":[{"value":"2008-11-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-03-12","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-05-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"542040"}}