Chng, Zhi Yee and Tan, Ta Sheng and Wong, Kok Bin
(2021)
*On the ramsey numbers for the tree graphs versus certain generalised wheel graphs.*
Discrete Mathematics, 344 (8).
ISSN 0012-365X,
DOI https://doi.org/10.1016/j.disc.2021.112440.

## Abstract

Given two simple graphs G and H, the Ramsey number R(G, H) is the smallest integer n such that for any graph of order n, either it contains G or its complement contains H. Let T-n be a tree graph of order n and W-s,W-m be the generalised wheel graph K-s + C-m. In this paper, we show that for n >= 5, s >= 2, R(T-n, W-s,W- 6) = (s + 1)(n - 1) + 1 and for n >= 5, s >= 1, R(T-n, W-s,W-7) = (s + 2)(n - 1) + 1. We also determine the exact value of R(T-n, W-s,W-m) for large nand s. (C) 2021 Elsevier B.V. All rights reserved.

Item Type: | Article |
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Funders: | UNSPECIFIED |

Uncontrolled Keywords: | Ramsey number; Tree; Generalised wheel graphs |

Subjects: | Q Science > QA Mathematics |

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

Depositing User: | Ms Zaharah Ramly |

Date Deposited: | 30 May 2022 07:37 |

Last Modified: | 30 May 2022 07:37 |

URI: | http://eprints.um.edu.my/id/eprint/27184 |

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