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Symmetry 2018, 10(12), 727; https://doi.org/10.3390/sym10120727

Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes

1
School of Mathematical Sciences, Anhui University, Hefei 230601, China
2
Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi, Swabi 23460, Pakistan
*
Author to whom correspondence should be addressed.
Received: 16 November 2018 / Revised: 3 December 2018 / Accepted: 4 December 2018 / Published: 6 December 2018
(This article belongs to the Special Issue Symmetry in Graph Theory)
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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. View Full-Text
Keywords: dominating set; binary locating-domination number; rotationally-symmetric convex polytopes; ILP models dominating set; binary locating-domination number; rotationally-symmetric convex polytopes; ILP models
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Raza, H.; Hayat, S.; Pan, X.-F. Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes. Symmetry 2018, 10, 727.

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