{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:47:46Z","timestamp":1753886866174,"version":"3.41.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,19]],"date-time":"2012-07-19T00:00:00Z","timestamp":1342656000000},"content-version":"vor","delay-in-days":200,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10871205"],"award-info":[{"award-number":["10871205"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010582","name":"Tianjin Polytechnic University","doi-asserted-by":"crossref","award":["10871205"],"award-info":[{"award-number":["10871205"]}],"id":[{"id":"10.13039\/501100010582","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The Merrifield\u2010Simmons index <jats:italic>i(G)<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of <jats:italic>G<\/jats:italic> The Hosoya index <jats:italic>z(G)<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> is defined as the total number of independent edge subsets, that is, the total number of its matchings. By <jats:italic>C<\/jats:italic>(<jats:italic>n<\/jats:italic>, <jats:italic>k<\/jats:italic>, <jats:italic>\u03bb<\/jats:italic>) we denote the set of graphs with <jats:italic>n<\/jats:italic> vertices, <jats:italic>k<\/jats:italic> cycles, the length of every cycle is <jats:italic>\u03bb<\/jats:italic>, and all the edges not on the cycles are pendant edges which are attached to the same vertex. In this paper, we investigate the Merrifield\u2010Simmons index <jats:italic>i(G)<\/jats:italic> and the Hosoya index <jats:italic>z(G)<\/jats:italic> for a graph <jats:italic>G<\/jats:italic> in <jats:italic>C<\/jats:italic>(<jats:italic>n<\/jats:italic>, <jats:italic>k<\/jats:italic>, <jats:italic>\u03bb<\/jats:italic>).<\/jats:p>","DOI":"10.1155\/2012\/520156","type":"journal-article","created":{"date-parts":[[2012,7,20]],"date-time":"2012-07-20T05:10:55Z","timestamp":1342761055000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Merrifield\u2010Simmons Index and Hosoya Index of <i>C<\/i>(<i>n<\/i>, <i>k<\/i>, <i>\u03bb<\/i>) Graphs"],"prefix":"10.1155","volume":"2012","author":[{"given":"Shaojun","family":"Dai","sequence":"first","affiliation":[]},{"given":"Ruihai","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,19]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/b100033"},{"volume-title":"Topological Methods in Chemistry","year":"1989","author":"Merrifield R. E.","key":"e_1_2_6_2_2"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1246\/bcsj.44.2322"},{"key":"e_1_2_6_4_2","first-page":"171","article-title":"The extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index","volume":"59","author":"Deng H.","year":"2008","journal-title":"MATCH Communications in Mathematical and in Computer Chemistry"},{"key":"e_1_2_6_5_2","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1515\/zna-2002-9-1006","article-title":"Extremal chemical trees","volume":"57","author":"Fischermann M.","year":"2002","journal-title":"Zeitschrift f\u00fcr Naturforschung Section B-A Journal of Chemical Sciences"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2004.07.001"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01164635"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(86)90015-6"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(01)00306-7"},{"key":"e_1_2_6_10_2","first-page":"221","article-title":"Extremal trees with respect to Hosoya index and Merrifield-Simmons index","volume":"57","author":"Wagner S. G.","year":"2007","journal-title":"MATCH Communications in Mathematical and in Computer Chemistry"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-70982-1"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2008.06.009"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.05.020"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/520156.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/520156.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/520156","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:09:55Z","timestamp":1718089795000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/520156"}},"subtitle":[],"editor":[{"given":"Ferenc","family":"Hartung","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/520156"],"URL":"https:\/\/doi.org\/10.1155\/2012\/520156","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2012-05-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-06-27","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-07-19","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"520156"}}