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Discussiones Mathematicae Graph Theory 21(1) (2001) 31-42
DOI: https://doi.org/10.7151/dmgt.1131

ON GRAPHS WITH A UNIQUE MINIMUM HULL SET

Gary Chartrand and Ping Zhang

Department of Mathematics and Statistics
Western Michigan University, Kalamazoo, MI 49008, USA

Abstract

We show that for every integer k ≥ 2 and every k graphs G₁, G₂,...,G_k, there exists a hull graph with k hull vertices v₁, v₂,...,v_k such that link L(v_i) = G_i for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a,b of integers with a ≥ 2 and b ≥ 0 is realizable as the hull number and forcing geodetic number of a hull graph.

Keywords: geodetic set, geodetic number, convex hull, hull set, hull number, hull graph.

References

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Received 8 March 2000
Revised 14 March 2001