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- Title
Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes.
- Authors
Raza, Hassan; Hayat, Sakander; Pan, Xiang-Feng
- Abstract
A convex polytope or simply polytope is the convex hull of a finite set of points in Euclidean space R d . Graphs of convex polytopes emerge from geometric structures of convex polytopes by preserving the adjacency-incidence relation between vertices. In this paper, we study the problem of binary locating-dominating number for the graphs of convex polytopes which are symmetric rotationally. We provide an integer linear programming (ILP) formulation for the binary locating-dominating problem of graphs. We have determined the exact values of the binary locating-dominating number for two infinite families of convex polytopes. The exact values of the binary locating-dominating number are obtained for two rotationally-symmetric convex polytopes families. Moreover, certain upper bounds are determined for other three infinite families of convex polytopes. By using the ILP formulation, we show tightness in the obtained upper bounds.
- Subjects
POLYTOPES; HYPERSPACE; GRAPH theory; EUCLIDEAN geometry; LINEAR programming
- Publication
Symmetry (20738994), 2018, Vol 10, Issue 12, p727
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym10120727