IJPAM: Volume 80, No. 3 (2012)



Government College of Engineering
Tirunelveli, 627 007, INDIA

Cape Institute of Technology
Levengipuram, 627114, INDIA
Abstract. For a connected graph , the hull number
of a graph
is the minimum cardinality of a set of vertices whose convex hull contains all vertices of
. A hull set
in a connected graph
is called a minimal hull set of
if no proper subset of
is a hull set of
. The upper hull number
of
is the maximum cardinality of a minimal hull set of
. Connected graphs of order
with upper hull number
or
are characterized. It is shown that for every integer
, there exists a connected graph
with
and
. A graph
is an extreme hull graph if
, that is if
has a unique minimum hull set consisting of the extreme vertices of
. It is shown that for every pair
,
of integers with
, there exists a connected extreme hull graph
such that
and
, where
is the geodetic number of a graph.
Received: March 11, 2012
AMS Subject Classification: 05C12
Key Words and Phrases: hull number, upper hull number, geodetic number
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 3