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On geodetic sets formed by boundary vertices
dc.contributor.author | Cáceres González, José |
dc.contributor.author | Hernando Martín, María del Carmen |
dc.contributor.author | Mora Giné, Mercè |
dc.contributor.author | Pelayo Melero, Ignacio Manuel |
dc.contributor.author | Puertas González, María Luz |
dc.contributor.author | Seara Ojea, Carlos |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-05-07T17:44:24Z |
dc.date.available | 2007-05-07T17:44:24Z |
dc.date.created | 2003 |
dc.date.issued | 2003 |
dc.identifier.uri | http://hdl.handle.net/2117/923 |
dc.description.abstract | Let G be a finite simple connected graph. A vertex v is a boundary vertex of G if there exists a vertex u such that no neighbor of v is further away from u than v. We obtain a number of properties involving different types of boundary vertices: peripheral, contour and eccentric vertices. Before showing that one of the main results in [3] does not hold for one of the cases, we establish a realization theorem that not only corrects the mentioned wrong statement but also improves it. Given S ⊆ V (G), its geodetic closure I[S] is the set of all vertices lying on some shortest path joining two vertices of S. We prove that the boundary vertex set ∂(G) of any graph G is geodetic, that is, I[∂(G)] = V (G). A vertex v belongs to the contour Ct(G) of G if no neighbor of v has an eccentricity greater than v. We present some sufficient conditions to guarantee the geodeticity of either the contour Ct(G) or its geodetic closure I[Ct(G)]. |
dc.format.extent | 16 |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject.lcsh | Graph theory |
dc.subject.lcsh | Convex geometry |
dc.subject.other | Boundary |
dc.subject.other | contour |
dc.subject.other | eccentricity |
dc.subject.other | geodesic convexity |
dc.subject.other | geodetic set |
dc.subject.other | periphery |
dc.title | On geodetic sets formed by boundary vertices |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.subject.lemac | Geometria convexa |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.subject.ams | Classificació AMS::52 Convex and discrete geometry::52A General convexity |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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