On graphs with a unique minimum hull set

Abstract

We show that for every integer k ‚ 2 and every k graphs G1; G2;:::;Gk, there exists a hull graph with k hull vertices v1;v2;:::;vk such that link L(vi) = Gi for 1 • ik. Moreover, every pair a;b of integers with 2 • ab 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.