Bondage number of grid graphs

Dettlaff, Magda; Lemańska, Magdalena; Yero, Ismael G.

doi:10.1016/j.dam.2013.11.020

Cited by 8 publications

(3 citation statements)

References 19 publications

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“…The study on graphs' locating-dominating set of was pioneered by Slater [1][2][3], which has been extended to total domination. Locating-total domination in graphs was firstly studied by Haynes et al [4], which has been further studied in References [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Locating-Total Domination Number in Strong Product of Two Paths

Kang¹,

Li²,

Li³

2020

dtcse

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In a monitoring system, each node's status is unique, and the system can accurately locate the node when there is a problem, which can be modeled through graphs' locating-total domination. When laying out the monitoring system, it is crucial to select the root node. Given a graph G, its locating-total domination number is the minimum cardinality of G's locating-total dominating set. In this paper, we give the bounds of this number for the strong product of two paths.

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Section: Introductionmentioning

confidence: 99%

Locating-Total Domination Number in Strong Product of Two Paths

Kang¹,

Li²,

Li³

2020

dtcse

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“…Recently, we have proved the Hamiltonian cycle (path) problem for supergrid graphs to be NP-complete [18]. For more works of investigation on grid and triangular grid graphs, we refer readers to [5,8,13,17,26,27,28,35].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian cycles in linear-convex supergrid graphs

Hung

2016

Discrete Applied Mathematics

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A supergrid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional supergrid. The supergrid graphs contain grid graphs and triangular grid graphs as subgraphs. The Hamiltonian cycle problem for grid and triangular grid graphs was known to be NP-complete. In the past, we have shown that the Hamiltonian cycle problem for supergrid graphs is also NP-complete. The Hamiltonian cycle problem on supergrid graphs can be applied to control the stitching trace of computerized sewing machines. In this paper, we will study the Hamiltonian cycle property of linear-convex supergrid graphs which form a subclass of supergrid graphs. A connected graph is called k-connected if there are k vertex-disjoint paths between every pair of vertices, and is called locally connected if the neighbors of each vertex in it form a connected subgraph. In this paper, we first show that any 2-connected, linear-convex supergrid graph is locally connected. We then prove that any 2-connected, linear-convex supergrid graph contains a Hamiltonian cycle.

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“…In addition, the Hamiltonian cycle problem on hexagonal grid graphs was known to be NP-complete [18]. For more related works, we refer readers to [5,7,9,13,15,16,17,24,27,28,29,36].…”

Section: Introductionmentioning

confidence: 99%

The Hamiltonian properties of supergrid graphs

Hung

Yao

Chan

2015

Theoretical Computer Science

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In this paper, we first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be NP-complete. However, they are unknown for supergrid graphs. The Hamiltonian cycle (path) problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines. In this paper, we will prove that the Hamiltonian cycle problem for supergrid graphs is NP-complete. It is easily derived from the Hamiltonian cycle result that the Hamiltonian path problem on supergrid graphs is also NP-complete. We then show that two subclasses of supergrid graphs, including rectangular (parallelism) and alphabet, always contain Hamiltonian cycles.

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Bondage number of grid graphs

Cited by 8 publications

References 19 publications

Locating-Total Domination Number in Strong Product of Two Paths

Locating-Total Domination Number in Strong Product of Two Paths

Hamiltonian cycles in linear-convex supergrid graphs

The Hamiltonian properties of supergrid graphs

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