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 Título: On geodetic sets formed by boundary vertices Cáceres González, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María Luz; Seara Ojea, Carlos Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions 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)]. Graph theoryConvex geometryBoundarycontoureccentricitygeodesic convexitygeodetic setperipheryGrafs, Teoria deGeometria convexaClassificació AMS::05 Combinatorics::05C Graph theoryClassificació AMS::52 Convex and discrete geometry::52A General convexity Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/ Artículo

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