Convexity in graphs and hypergraphs
SIAM Journal on Algebraic and Discrete Methods
The primitivity of the strong product of two directed graphs
Discrete Mathematics
Pancyclicity of Strong Products of Graphs
Graphs and Combinatorics
Geodeticity of the contour of chordal graphs
Discrete Applied Mathematics
Hamiltonian threshold for strong products of graphs
Journal of Graph Theory
The geodetic number of a graph
Mathematical and Computer Modelling: An International Journal
On the hull number of some graph classes
Theoretical Computer Science
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A set S of vertices of a connected graph G is convex, if for any pair of vertices u,v@?S, every shortest path joining u and v is contained in S. The convex hull CH(S) of a set of vertices S is defined as the smallest convex set in G containing S. The set S is geodetic, if every vertex of G lies on some shortest path joining two vertices in S, and it is said to be a hull set if its convex hull is V(G). The geodetic and the hull numbers of G are the minimum cardinality of a geodetic and a minimum hull set, respectively. In this work, we investigate the behavior of both geodetic and hull sets with respect to the strong product operation for graphs. We also establish some bounds for the geodetic number and the hull number and obtain the exact value of these parameters for a number of strong product graphs.