{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,28]],"date-time":"2024-07-28T13:52:59Z","timestamp":1722174779757},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,10]]},"abstract":"<jats:p> The square of a graph [Formula: see text] is the graph obtained from [Formula: see text] by adding edges joining those pairs of vertices whose distance from each other in [Formula: see text] is two. If [Formula: see text] is connected, then the cyclomatic number of [Formula: see text] is defined as [Formula: see text]. Graphs with cyclomatic number not more than [Formula: see text] whose square are panconnected have been characterized, among other things, in [G. L. Chia, S. H. Ong and L. Y. Tan, On graphs whose square have strong Hamiltonian properties, Discrete Math. 309 (2009) 4608\u20134613, G. L. Chia, W. Hemakul and S. Singhun, Graphs with cyclomatic number two having panconnected square, Discrete Math. 311 (2011) 850\u2013855]. Here, we show that if [Formula: see text] has cyclomatic number [Formula: see text] and [Formula: see text] is panconnected, then [Formula: see text] is one of the eight families of graphs, [Formula: see text], defined in the paper. Further, we obtain necessary and sufficient conditions for three larger families of graphs (which contains [Formula: see text] as special cases) whose square are panconnected. <\/jats:p>","DOI":"10.1142\/s1793830917500677","type":"journal-article","created":{"date-parts":[[2017,9,28]],"date-time":"2017-09-28T04:13:08Z","timestamp":1506571988000},"page":"1750067","source":"Crossref","is-referenced-by-count":2,"title":["Graphs with cyclomatic number three having panconnected square"],"prefix":"10.1142","volume":"09","author":[{"given":"G. L.","family":"Chia","sequence":"first","affiliation":[{"name":"Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Sungai Long, Malaysia"},{"name":"Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia"}]},{"given":"W.","family":"Hemakul","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand"}]},{"given":"S.","family":"Singhun","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand"},{"name":"Centre of Excellence in Mathematics, CHE, Si Ayuthaya Rd., Bangkok 10400, Thailand"}]}],"member":"219","published-online":{"date-parts":[[2017,11,2]]},"reference":[{"key":"S1793830917500677BIB001","first-page":"19","volume":"10","author":"Alavi Y.","year":"1975","journal-title":"Stud. Sci. Math. Hung."},{"key":"S1793830917500677BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90075-6"},{"key":"S1793830917500677BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.01.030"},{"key":"S1793830917500677BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.02.026"},{"key":"S1793830917500677BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(76)90065-4"},{"key":"S1793830917500677BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01305995"},{"key":"S1793830917500677BIB007","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300008494"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830917500677","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T05:24:46Z","timestamp":1565155486000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500677"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10]]},"references-count":7,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2017,11,2]]},"published-print":{"date-parts":[[2017,10]]}},"alternative-id":["10.1142\/S1793830917500677"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500677","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10]]}}}