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Title:	Some structural, metric and convex properties of the boundary of a graph
Author:	Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Seara Ojea, Carlos
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
Abstract:	Let u;v be two vertices of a connected graph G . The vertex v is said to be a boundary vertex of u if no neighbor of v is further away from u than v . The boundary of a graph is the set of all its boundary vertices. In this work, we present a number of properties of the boundary of a graph under diÆerent points of view: (1) a realization theorem involving diÆerent types of boundary vertex sets: extreme set, periphery, contour, and the whole boundary; (2) the contour is a monophonic set; and (3) the cardinality of the boundary is an upper bound for both the metric dimension and the determining number of a graph
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Convex geometry -Boundary -Contour -Extreme set -Graph convexity -Metric dimension. -Geometria convexa
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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