{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:24:22Z","timestamp":1761963862327,"version":"build-2065373602"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> For any two vertices u and v in a connected graph G, a u \u2013 v path is a monophonic path if it contains no chords, and the monophonic distance d<jats:sub>m<\/jats:sub>(u, v) from u to v is defined as the length of a longest u \u2013 v monophonic path in G. A u \u2013 v monophonic path of length d<jats:sub>m<\/jats:sub>(u, v) is called a u \u2013 v monophonic. The monophonic eccentricity e<jats:sub>m<\/jats:sub>(v) of a vertex v in G is the maximum monophonic distance from v to a vertex of G. The monophonic radius rad <jats:sub>m<\/jats:sub> G of G is the minimum monophonic eccentricity among the vertices of G, while the monophonic diameter diam <jats:sub>m<\/jats:sub> G of G is the maximum monophonic eccentricity among the vertices of G. It is shown that rad <jats:sub>m<\/jats:sub> G \u2264 diam <jats:sub>m<\/jats:sub> G for every connected graph G and that every pair a, b of positive integers with a \u2264 b is realizable as the monophonic radius and monophonic diameter of some connected graph. Also, for any three positive integers a, b and c with 3 \u2264 a \u2264 b \u2264 c, there is a connected graph G such that rad G = a, rad <jats:sub>m<\/jats:sub> G = b and rad <jats:sub>D<\/jats:sub>G = c; and for any three positive integers a, b and c with 5 \u2264 a \u2264 b \u2264 c, there is a connected graph G such that diam G = a, diam <jats:sub>m<\/jats:sub> G = b and diam <jats:sub>D<\/jats:sub> G = c, where rad G, diam G, rad <jats:sub>D<\/jats:sub>G and diam <jats:sub>D<\/jats:sub> G denote the radius, diameter, detour radius and detour diameter, respectively. The monophonic center of G is the subgraph induced by the vertices of G having monophonic eccentricity rad <jats:sub>m<\/jats:sub> G and it is shown that every graph is the monophonic center of some connected graph and also that the monophonic center C<jats:sub>m<\/jats:sub>(G) of every connected graph G is a subgraph of some block of G. <\/jats:p>","DOI":"10.1142\/s1793830911001176","type":"journal-article","created":{"date-parts":[[2011,7,13]],"date-time":"2011-07-13T13:20:39Z","timestamp":1310563239000},"page":"159-169","source":"Crossref","is-referenced-by-count":17,"title":["MONOPHONIC DISTANCE IN GRAPHS"],"prefix":"10.1142","volume":"03","author":[{"given":"A. P.","family":"SANTHAKUMARAN","sequence":"first","affiliation":[{"name":"Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai 627 002, India"}]},{"given":"P.","family":"TITUS","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Anna University Tirunelveli, Tirunelveli 627 007, India"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","first-page":"269","volume":"18","author":"Bielak H.","journal-title":"Studia Sci. Math. Hungar."},{"volume-title":"Distance in Graphs","year":"1990","author":"Buckley F.","key":"rf2"},{"key":"rf3","first-page":"75","volume":"53","author":"Chartrand G.","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf4","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"Harary F.","year":"1969"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2307\/1969824"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(73)90116-7"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911001176","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:13:03Z","timestamp":1565194383000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911001176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6]]},"references-count":6,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,6]]}},"alternative-id":["10.1142\/S1793830911001176"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911001176","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2011,6]]}}}