{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T04:17:39Z","timestamp":1728274659772},"reference-count":0,"publisher":"Combinatorial Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>A path \\(x_1, x_2, \\dots, x_n\\) in a connected graph \\( G \\) that has no edge \\( x_i x_j \\) \\((j \\geq i+3)\\) is called a monophonic-triangular path or mt-path. A non-empty subset \\( M \\) of \\( V(G) \\) is a monophonic-triangular set or mt-set of \\( G \\) if every member in \\( V(G) \\) exists in a mt-path joining some pair of members in \\( M \\). The monophonic-triangular number or mt-number is the lowest cardinality of an mt-set of \\( G \\) and it is symbolized by \\( mt(G) \\). The general properties satisfied by mt-sets are discussed. Also, we establish \\( mt \\)-number boundaries and discover similar results for a few common graphs. Graphs \\( G \\) of order \\( p \\) with \\( mt(G) = p \\), \\( p \u2013 1 \\), or \\( p \u2013 2 \\) are characterized.<\/jats:p>","DOI":"10.61091\/ars-160-11","type":"journal-article","created":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T21:36:01Z","timestamp":1728250561000},"page":"117-126","source":"Crossref","is-referenced-by-count":0,"title":["The Monophonic-triangular Number of a Graph"],"prefix":"10.61091","volume":"160","author":[{"name":"Department of Science and Humanities, St.Mother Theresa Engineering College, Thoothukudi 628 102, India","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.Princeton","family":"Lazarus","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"Selvakumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Science and Humanities, University College of Engineering Nagercoil, Anna University: Tirunelveli Region, Nagercoil \u2013 629 004, India","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Titus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Science and Humanities, University College of Engineering Nagercoil, Anna University: Tirunelveli Region, Nagercoil \u2013 629 004, India","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2024,9,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T21:36:09Z","timestamp":1728250569000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-160\/the-monophonic-triangular-number-of-a-graph\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,9,30]]},"published-print":{"date-parts":[[2024,9,30]]}},"URL":"https:\/\/doi.org\/10.61091\/ars-160-11","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,30]]}}}