图的圈和树孤立

张刚; 吴宝音都仍

doi:10.13568/j.cnki.651094.651316.2021.03.06.0004

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图的圈和树孤立

更新时间：2026-01-21

- 图的圈和树孤立
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 39, Issue 2, Pages: 169-175(2022)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2021.03.06.0004
  CLC： O157.5
- Published：2022
- 稿件说明：
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[1]张刚,吴宝音都仍.图的圈和树孤立[J].新疆大学学报(自然科学版)(中英文),2022,39(02):169-175.
[1]张刚,吴宝音都仍.图的圈和树孤立[J].新疆大学学报(自然科学版)(中英文),2022,39(02):169-175. DOI： 10.13568/j.cnki.651094.651316.2021.03.06.0004.

DOI：10.13568/j.cnki.651094.651316.2021.03.06.0004.

摘要

对任一图G

如果顶点子集D使得G-N[D]不包含任何一个F中的F图作为子图

那么D被叫做图G的一个F孤立集

其中F是一个连通图集.图G中最小的一个F孤立集D的阶数被称为图G的F孤立数

记为ι(G

F).特别的

当F={C3

P4}时

定义ι(G

{C3

P4})=ι′c(G).于是

图G中任一{C3

P4}孤立集D使得G-N [D]只是一些K1

K2和P3分支

而ιc~′(G)表示图G中最小的一个{C3

P4}孤立集D的阶数.本文证明了如果G?{C3

C7}是一个顶点数为n的连通图

那么ι′c(G)≤n/4

且这个上界是最好的.

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 byι(G

is the minimum cardinality of an F-isolating set in G. In this paper

take F = {C3

P4} and denoteι(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

thenι′c(G) ≤4 n.

关键词

Keywords

references

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