@article{ZHANG2022, 
author = {Gang ZHANG and Baoyindureng WU},
title = {Isolation of Cycles and Trees in Graphs},
year = {2022},
journal = {Journal of Xinjiang University(Natural Science Edition in Chinese and English)},
volume = {39},
number = {2},
pages = {169-175},
keywords = {isolation number, cycles, trees, partial domination},
url = {https://www.sciopen.com/article/10.13568/j.cnki.651094.651316.2021.03.06.0004},
doi = {10.13568/j.cnki.651094.651316.2021.03.06.0004},
abstract = {A subset D ⊆ V (G) is called an  F-isolating set of a graph G if G−N[D] contains no subgraph isomorphic to any F ∈  F, where  F is a family of connected graphs. The  F-isolation number of G, denoted by ι(G, F), is the minimum cardinality of an  F-isolating set in G. In this paper, take  F = {C3,K1,3,P4} and denote ι(G, F) simply by  ι′c,(G) which implies that  ι′c(G) is the order of a smallest set D such that G−N[D] consists of some K1, K2 and P3 only. We prove that if G is a connected graph of order n and different from C3 or C7, then  ι′c(G)≤ n4.}
}