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On the Geodetic Hull Number of Complementary Prisms
Let be a finite, simple, and undirected graph and let be a set of
vertices of . In the geodetic convexity, a set of vertices of a graph
is convex if all vertices belonging to any shortest path between two
vertices of lie in . The convex hull of is the smallest
convex set containing . If , then is a hull set. The
cardinality of a minimum hull set of is the hull number of . The
complementary prism of a graph arises from the disjoint
union of the graph and by adding the edges of a perfect
matching between the corresponding vertices of and .
Motivated by previous work, we determine and present lower and upper bounds on
the hull number of complementary prisms of trees, disconnected graphs and
cographs. We also show that the hull number on complementary prisms cannot be
limited in the geodetic convexity, unlike the -convexity.Comment: 12 pages, 5 figure