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Locating-dominating number of certain infinite families of convex polytopes with applications
- Source :
- Heliyon, Vol 10, Iss 8, Pp e29304- (2024)
- Publication Year :
- 2024
- Publisher :
- Elsevier, 2024.
-
Abstract
- A convex hull of finitely many points in the Euclidean space Rd is known as a convex polytope. Graphically, they are planar graphs i.e. embeddable on R2. Minimum dominating sets possess diverse applications in computer science and engineering. Locating-dominating sets are a natural extension of dominating sets. Studying minimizing locating-dominating sets of convex polytopes reveal interesting distance-dominating related topological properties of these geometrical planar graphs. In this paper, exact value of the locating-dominating number is shown for one infinite family of convex polytopes. Moreover, tight upper bounds on γl−d are shown for two more infinite families. Tightness in the upper bounds is shown by employing an updated integer linear programming (ILP) model for the locating-dominating number γl−d of a fixed graph. Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of ρ>0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number γl−d delivers such a strong prediction potential. The paper is concluded with putting forward some open problems in this area.
Details
- Language :
- English
- ISSN :
- 24058440
- Volume :
- 10
- Issue :
- 8
- Database :
- Directory of Open Access Journals
- Journal :
- Heliyon
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.9cc7424f20b14c38ae55f3f2a54ccba7
- Document Type :
- article
- Full Text :
- https://doi.org/10.1016/j.heliyon.2024.e29304