Arbitrarily large neighborly families of symmetric convex polytopes

1986 ◽  
Vol 20 (2) ◽  
pp. 175-179 ◽  
Author(s):  
Joseph Zaks
Keyword(s):  
Convex Polytopes ◽  
Symmetric Convex ◽  
Neighborly Families

scholarly journals Non-symmetric convex polytopes and Gabor orthonormal bases

2018 ◽  
Vol 146 (12) ◽  
pp. 5147-5155
Author(s):  
Randolf Chung ◽  
Chun-kit Lai
Keyword(s):  
Convex Polytopes ◽  
Symmetric Convex ◽  
Orthonormal Bases

Asymmetry of Convex Polytopes and Vertex Index of Symmetric Convex Bodies

2008 ◽  
Vol 40 (4) ◽  
pp. 528-536 ◽  
Author(s):  
E. D. Gluskin ◽  
A. E. Litvak
Keyword(s):  
Convex Polytopes ◽  
Convex Bodies ◽  
Symmetric Convex ◽  
Vertex Index

scholarly journals Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 727 ◽  
Author(s):  
Hassan Raza ◽  
Sakander Hayat ◽  
Xiang-Feng Pan
Keyword(s):  
Convex Polytopes ◽  
Convex Polytope ◽  
Upper Bounds ◽  
Symmetric Convex ◽  
Dominating Sets ◽  
Incidence Relation ◽  
Dominating Number ◽  
Rotationally Symmetric ◽  
Finite Set ◽  
Set Of Points

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.

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