## 摘要

Let G be a connected graph, and let D(G) be the set of all dominating (multi)sets for G. For D_{1} and D_{2} in D(G), we say that D_{1} is single-step transferable to D_{2} if there exist u∈D_{1} and v∈D_{2}, such that uv∈E(G) and D_{1}−{u}=D_{2}−{v}. We write D_{1}⟶∗D_{2} if D_{1} can be transferred to D_{2} through a sequence of single-step transfers. We say that G is k-transferable if D_{1}⟶∗D_{2} for any D_{1},D_{2}∈D(G) with |D_{1}|=|D_{2}|=k. The transferable domination number of G is the smallest integer k to guarantee that G is l-transferable for all l≥k. We study the transferable domination number of graphs in this paper. We give upper bounds for the transferable domination number of general graphs and bipartite graphs, and give a lower bound for the transferable domination number of grids. We also determine the transferable domination number of P_{m}×P_{n} for the cases that m=2,3, or mn≡0(mod6). Besides these, we give an example to show that the gap between the transferable domination number of a graph G and the smallest number k so that G is k-transferable can be arbitrarily large.

原文 | ???core.languages.en_GB??? |
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頁（從 - 到） | 135-146 |

頁數 | 12 |

期刊 | Discrete Applied Mathematics |

卷 | 313 |

DOIs | |

出版狀態 | 已出版 - 31 5月 2022 |