{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:15Z","timestamp":1740134535490,"version":"3.37.3"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T00:00:00Z","timestamp":1570060800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002842","name":"Chiang Mai University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002842","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2019,10,3]]},"abstract":"<jats:p>In this study, we work on the Fuchsian group <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>H<\/mml:mi><mml:msqrt><mml:mi>m<\/mml:mi><\/mml:msqrt><\/mml:mrow><\/mml:math> where <jats:italic>m<\/jats:italic> is a prime number acting on <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msqrt><mml:mi>m<\/mml:mi><\/mml:msqrt><mml:mrow><mml:mover accent=\"true\"><mml:mi>\u211a<\/mml:mi><mml:mo>^<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:mrow><\/mml:math> transitively. We give necessary and sufficient conditions for two vertices to be adjacent in suborbital graphs induced by these groups. Moreover, we investigate infinite paths of minimal length in graphs and give the recursive representation of continued fraction of such vertex.<\/jats:p>","DOI":"10.1155\/2019\/7652729","type":"journal-article","created":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T19:30:45Z","timestamp":1570131045000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Infinite Paths of Minimal Length on Suborbital Graphs for Some Fuchsian Groups"],"prefix":"10.1155","volume":"2019","author":[{"given":"Khuanchanok","family":"Chaichana","sequence":"first","affiliation":[{"name":"Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2700-3212","authenticated-orcid":true,"given":"Pradthana","family":"Jaipong","sequence":"additional","affiliation":[{"name":"Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/bf01565437"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1977.70.481"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1215\/s0012-7094-54-02154-7"},{"issue":"2","key":"4","first-page":"275","volume":"19","year":"1999","journal-title":"Note di Matematica"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1017\/cbo9780511661846.006"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/bf01117534"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1112\/s0024609301008311"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1090\/s1088-4173-07-00172-5"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/s0012-365x(00)00191-6"},{"year":"2008","key":"10"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/7652729.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/7652729.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/7652729.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T19:30:46Z","timestamp":1570131046000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2019\/7652729\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,3]]},"references-count":10,"alternative-id":["7652729","7652729"],"URL":"https:\/\/doi.org\/10.1155\/2019\/7652729","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2019,10,3]]}}}