Let a set of vertices 
in a connected graph 
be called convex if for every two vertices 
, the vertex set of every 
graph geodesic lies
completely in 
.
Also define the convex hull 
of a graph 
with vertex set 
as the smallest convex set
in 
containing 
. Then the smallest cardinality of a set 
whose convex hull is 
is called the hull number of 
, denoted 
.
Hull Number
See also
Geodetic NumberExplore with Wolfram|Alpha
References
Chartrand, G. and Zhang, P. "The Forcing Hull Number of a Graph." J. Combin. Math. Comb. Comput. 36, 81-94, 2001.Chartrand, G. and Zhang, P. "The Geodetic Number of an Oriented Graph." Europ. J. Combin. 21, 181-189, 2000.Chartrand, G.; Harary, F.; and Zhang, P. "On the Hull Number of a Graph." Ars. Combin. 57, 129-138, 2000.Everett, M. G. and Seidman, S. B. "The Hull Number of a Graph." Discr. Math. 57, 217-223, 1985.Mulder, H. M. "The Expansion Procedure for Graphs." In Contemporary Methods in Graph Theory (Ed. R. Bodendiek). Mannheim, Germany: Wissenschaftsverlag, pp. 459-477, 1990.Referenced on Wolfram|Alpha
Hull NumberCite this as:
Weisstein, Eric W. "Hull Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HullNumber.html