Convexity, geodetic, and hull numbers of the join of graphs

Authors

Sergio R. Canoy Jr., MSU-Iligan Institute of Technology
Gilbert B. Cagaanan, MSU-Iligan Institute of Technology
Severino V. Gervacio, De La Salle University, Manila

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Archival Material/Manuscript

Publication Date

2006

Abstract

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 [1] 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 [5] by obtaining a more elegant expression for the hull number of the join G + Km̈, where G is a connected non-complete graph.

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Recommended Citation

Canoy, S. R., Cagaanan, G. B., & Gervacio, S. V. (2006). Convexity, geodetic, and hull numbers of the join of graphs. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/6608

Disciplines

Mathematics

Note

Publication/creation date supplied

Keywords

Convex sets; Convex domains

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