Some structural, metric and convex properties of the boundary of a graph
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hdl:2117/20898
Tipus de documentArticle
Data publicació2013-04-25
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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
CitacióHernando, 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.
ISSN0381-7032
Versió de l'editorhttp://www.combinatorialmath.ca/arscombinatoria/vol109.html
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