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dc.contributor.authorTitus, P.en_US
dc.contributor.authorSanthakumaran, A. P.en_US
dc.contributor.authorGanesamoorthy, K.en_US
dc.date.accessioned2020-10-07T10:05:45Z
dc.date.available2020-10-07T10:05:45Z
dc.date.issued2016
dc.identifier.citationTitus, P., Santhakumaran, A. P. & Ganesamoorthy, K. (2016). The connected detour monophonic number of a graph. TWMS Journal of Applied and Engineering Mathematics, 6(1), 75-86.en_US
dc.identifier.issn2146-1147en_US
dc.identifier.issn2587-1013en_US
dc.identifier.urihttp://belgelik.isikun.edu.tr/xmlui/handle/iubelgelik/2580
dc.identifier.urihttp://jaem.isikun.edu.tr/web/index.php/archive/91-vol6no1/236
dc.description.abstractFor a connected graph G = (V, E) of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A longest x ? y monophonic path is called an x ? y detour monophonic path. A set S of vertices of G is a detour monophonic set of G if each vertex v of G lies on an x ? y detour monophonic path, for some x and y in S. The minimum cardinality of a detour monophonic set of G is the detour monophonic number of G and is denoted by dm(G). A connected detour monophonic set of G is a detour monophonic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected detour monophonic set of G is the connected detour monophonic number of G and is denoted by dmc(G). We determine bounds for dmc(G) and characterize graphs which realize these bounds. It is shown that for positive integers r, d and k ? 6 with r < d, there exists a connected graph G with monophonic radius r, monophonic diameter d and dmc(G) = k. For each triple a, b, p of integers with 3 ? a ? b ? p ? 2, there is a connected graph G of order p, dm(G) = a and dmc(G) = b. Also, for every pair a, b of positive integers with 3 ? a ? b, there is a connected graph G with mc(G) = a and dmc(G) = b, where mc(G) is the connected monophonic number of G.en_US
dc.description.sponsorshipThe first author is partially supported by DST Project No. SR/S4/MS:570/09.en_US
dc.language.isoenen_US
dc.publisherIşık University Pressen_US
dc.relation.ispartofTWMS Journal of Applied and Engineering Mathematicsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
dc.subjectDetour monophonic seten_US
dc.subjectDetour monophonic numberen_US
dc.subjectConnected detour monophonic seten_US
dc.subjectConnected detour monophonic numberen_US
dc.titleThe connected detour monophonic number of a graphen_US
dc.typeArticleen_US
dc.description.versionPublisher's Versionen_US
dc.identifier.volume6
dc.identifier.issue1
dc.identifier.startpage75
dc.identifier.endpage86
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıen_US


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