On the Steiner, geodetic and hull numbers of graphs

DOI10.1016/j.disc.2004.08.039zbMath1062.05052OpenAlexW2102217150MaRDI QIDQ1779492

Ignacio M. Pelayo, Tao Jiang, Carmen Hernando, Carlos Seara, Mercè Mora

Publication date: 1 June 2005

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2117/868

zbMATH Keywords

convexitygeodesicchordal graphgeodetic numberSteiner numberSteiner setgeodetic sethull numbermonophonic set

Mathematics Subject Classification ID

Distance in graphs (05C12)

Related Items (36)

On geodetic sets formed by boundary vertices ⋮ On the \(P_3\)-hull number of some products of graphs ⋮ Monophonic numbers of the join and composition of connected graphs ⋮ Some Steiner concepts on lexicographic products of graphs ⋮ On the toll number of a graph ⋮ Algorithms and complexity for geodetic sets on partial grids ⋮ Convexity in partial cubes: the hull number ⋮ Unnamed Item ⋮ Toll number of the strong product of graphs ⋮ Unnamed Item ⋮ A note on the geodetic number and the Steiner number of AT-free graphs ⋮ Some properties of the intersection graph for finite commutative principal ideal rings ⋮ Convex sets in lexicographic products of graphs ⋮ On the (M, D) number of a graph ⋮ Graphs with a minimal number of convex sets ⋮ On pitfalls in computing the geodetic number of a graph ⋮ A survey on the Intersection graphs of ideals of rings ⋮ Geodeticity of the contour of chordal graphs ⋮ Toll convexity ⋮ Some remarks on the geodetic number of a graph ⋮ Toll number of the Cartesian and the lexicographic product of graphs ⋮ Strong geodetic problem in grid-like architectures ⋮ Strong geodetic problem in networks ⋮ Polynomial Time Algorithms for Computing a Minimum Hull Set in Distance-Hereditary and Chordal Graphs ⋮ Hull and geodetic numbers for some classes of oriented graphs ⋮ Hull and geodetic numbers for some classes of oriented graphs ⋮ The vertex steiner number of a graph ⋮ The upper restrained Steiner number of a graph ⋮ Generating all the Steiner trees and computing Steiner intervals for a fixed number of terminals ⋮ Steiner intervals, geodesic intervals, and betweenness ⋮ Geodetic number of powers of cycles ⋮ On the vertex monophonic, vertex geodetic and vertex Steiner numbers of graphs ⋮ Connected monophonic domination in graphs ⋮ Some structural, metric and convex properties on the boundary of a graph ⋮ The restrained geodetic number of a graph ⋮ THE FORCING EDGE FIXING EDGE-TO-VERTEX MONOPHONIC NUMBER OF A GRAPH

Cites Work

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• Unnamed Item
• Characterizations of strongly chordal graphs
• On local convexity in graphs
• The geodetic number of a graph
• Comment on ``The Steiner number of a graph by G. Chartrand and P. Zhang [Discrete Mathematics 242 (2002) 41--54]
• Representation of a finite graph by a set of intervals on the real line
• Convexity in Graphs and Hypergraphs
• A characterization of ptolemaic graphs
• A CHARACTERIZATION OF DISTANCE-HEREDITARY GRAPHS
• Convexity and HHD-Free Graphs
• Asteroidal Triple-Free Graphs
• The Steiner number of a graph

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