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Some structural, metric and convex properties of the boundary of a graph

Author
Hernando, M.; Mora, M.; Pelayo, I. M.; Seara, C.
Type of activity
Journal article
Journal
Ars combinatoria
Date of publication
2013-04-25
Volume
109
First page
267
Last page
283
Repository
http://hdl.handle.net/2117/20898 Open in new window
URL
http://www.combinatorialmath.ca/arscombinatoria/vol109.html Open in new window
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...
Citation
Hernando, M. [et al.]. Some structural, metric and convex properties of the boundary of a graph. "Ars combinatoria", 25 Abril 2013, vol. 109, p. 267-283.
Keywords
Boundary, Contour, Extreme set, Graph convexity, Metric dimension.
Group of research
CGA -Computational Geometry and Applications
COMBGRAPH - Combinatorics, Graph Theory and Applications
DCG - Discrete and Combinatorial Geometry

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