Convexity, geodetic, and hull numbers of the join of graphs
College of Science
Mathematics and Statistics Department
In this paper, we characterize the convex sets in the join of two graphs in a more general setting and determine its convexity number. We also show that a result in  concerning the geodetic number of the join of graphs does not always hold. In particular, we show that the geodetic number of the join of any two connected non-complete graphs is either 2, 3 or 4. Further, we characterize those joins which yield geodetic number equal to 2 and those with geodetic number equal to 3. Finally, we define and use the concept of 2-path closure absorbing set in a graph to characterize the hull sets in G + Km. We improve and correct a result in  by obtaining a more elegant expression for the hull number of the join G + Km̈, where G is a connected non-complete graph.
Canoy, S. R., Cagaanan, G. B., & Gervacio, S. V. (2006). Convexity, geodetic, and hull numbers of the join of graphs. Utilitas Mathematica, 71, 143-159. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/4606
Convex sets; Convex domains