The binary locating-dominating number of some convex polytopes

Simić, Ana; Bogdanović, Milena; Milošević, Jelisavka

doi:10.26493/1855-3974.973.479

Cited by 12 publications

(8 citation statements)

References 22 publications

(26 reference statements)

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“…Raza et al [20]). e binary locating-dominating number of convex polytopes is studied by Simić et al [21] and Raza et al [22]. e open-locatingdominating number of certain convex polytopes has recently been studied by Savić et al [23].…”

Section: E(g) ⊆mentioning

confidence: 99%

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

Hayat

Malik

Ahmad

et al. 2021

Mathematical Problems in Engineering

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A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamilton-connected if there exists at least one Hamiltonian path between any of its two vertices. The detour index is defined to be the sum of the lengths of longest distances, i.e., detours between vertices in a graph. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering, whereas the detour index has important applications in chemistry. Checking whether a graph is Hamilton-connected and computing the detour index of an arbitrary graph are both NP-complete problems. In this paper, we study these problems simultaneously for certain families of convex polytopes. We construct two infinite families of Hamilton-connected convex polytopes. Hamilton-connectivity is shown by constructing Hamiltonian paths between any pair of vertices. We then use the Hamilton-connectivity to compute the detour index of these families. A family of non-Hamilton-connected convex polytopes has also been constructed to show that not all convex polytope families are Hamilton-connected.

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Section: E(g) ⊆mentioning

confidence: 99%

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

Hayat

Malik

Ahmad

et al. 2021

Mathematical Problems in Engineering

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“…All these classes are called convex polytopes and for all of them in the mentioned papers were given their metric dimensions. As introduced in [14], the problem of binary locating domination is related to that of open locating domination. In [14] the exact values of the binary locating-dominating number for convex polytopes D n , and R n are determined as well as the tight bounds for R n , Q n and U n .…”

Section: Theorem 18 [4]mentioning

confidence: 99%

The open-locating-dominating number of some convex polytopes

Lj.

Bogdanovic

2018

Filomat

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In this paper we will investigate the problem of finding the open-locating-dominating number for some classes of planar graphs-convex polytopes. We considered D n , T n , B n , C n , E n and R n classes of convex polytopes known from the literature. The exact values of open-locating-dominating number for D n and R n polytopes are presented, along with the upper bounds for T n , B n , C n , and E n polytopes.

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“…Samlan et al [22] considered three optimization problems, known as the local metric, the fault-tolerant metric and the strong metric dimension problem, for two infinite families of convex polytopes. Simić et al [23] studied the problem of binary locating-dominating number of some convex polytopes. The ILP model presented in the next section was essentially given by Simić et al [23].…”

Section: Theorem 1 [11]mentioning

confidence: 99%

“…Simić et al [23] studied the problem of binary locating-dominating number of some convex polytopes. The ILP model presented in the next section was essentially given by Simić et al [23]. Other graph-theoretic parameters having potential applications in chemistry are studied in [24][25][26][27].…”

Section: Theorem 1 [11]mentioning

confidence: 99%

Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes

2018

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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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The binary locating-dominating number of some convex polytopes

Abstract: In this paper the binary locating-dominating number of convex polytopes is considered. The exact value is determined and proved for convex polytopes D n and R n , while for the convex polytopes R n , Q n and U n a tight upper bound of the locating-dominating number is presented.

Cited by 12 publications

References 22 publications

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes

The open-locating-dominating number of some convex polytopes

Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes

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