Sim, Kai An and Tan, Ta Sheng and Wong, Kok Bin
(2018)
*On the minimum order of 4-lazy cops-win graphs.*
Bulletin of the Korean Mathematical Society, 55 (6).
pp. 1667-1690.
ISSN 1015-8634,
DOI https://doi.org/10.4134/BKMS.b170948.

## Abstract

We consider the minimum order of a graph G with a given lazy cop number c L (G). Sullivan, Townsend and Werzanski [7] showed that the minimum order of a connected graph with lazy cop number 3 is 9 and K 3 □K 3 is the unique graph on nine vertices which requires three lazy cops. They conjectured that for a graph G on n vertices with ∆(G) ≥ n − k 2 , c L (G) ≤ k. We proved that the conjecture is true for k = 4. Furthermore, we showed that the Petersen graph is the unique connected graph G on 10 vertices with ∆(G) ≤ 3 having lazy cop number 3 and the minimum order of a connected graph with lazy cop number 4 is 16.

Item Type: | Article |
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Funders: | Postgraduate Research Grant (PPP)-Research PG068-2015A by University of Malaya |

Uncontrolled Keywords: | Cops and Robbers; vertex-pursuit games; minimum order |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |

Divisions: | Faculty of Science > Institute of Mathematical Sciences |

Depositing User: | Ms. Juhaida Abd Rahim |

Date Deposited: | 12 Mar 2019 02:03 |

Last Modified: | 12 Mar 2019 02:03 |

URI: | http://eprints.um.edu.my/id/eprint/20660 |

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