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On the geodetic and the hull numbers in strong product graphs
Cáceres, Jose; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María Luz
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. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions; Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
A set S of vertices of a connected graph G is convex, if for any pair of vertices u,vS, every shortest path joining u and v is contained in S. The convex hull CH(S) of a set of vertices S is defined as the smallest convex set in G containing S. The set S is geodetic, if every vertex of G lies on some shortest path joining two vertices in S, and it is said to be a hull set if its convex hull is V(G). The geodetic and the hull numbers of G are the minimum cardinality of a geodetic and a minimum hull set, respectively. In this work, we investigate the behavior of both geodetic and hull sets with respect to the strong product operation for graphs. We also establish some bounds for the geodetic number and the hull number and obtain the exact value of these parameters for a number of strong product graphs.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística
Graph theory
Grafs, Teoria de
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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