关于直积图的坚韧度和边坚韧度的注记（英文）

热西旦·湖加

doi:10.13568/j.cnki.651094.2016.04.006

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关于直积图的坚韧度和边坚韧度的注记（英文）

数理科学 | 更新时间：2026-01-21

- 关于直积图的坚韧度和边坚韧度的注记（英文）
- 关于直积图的坚韧度和边坚韧度的注记（英文）
- 新疆大学学报（自然科学版中英文） 2016年33卷第4期页码：407-410
- 作者机构：
  
  1. 福州大学离散数学研究中心
  2. 新疆财经大学应用数学学院
- 作者简介：
- 基金信息：
  
  supported by NSFC(11361060);the Research Fund of Xinjiang University of Finance and Economics(2014XYB008)
- DOI：10.13568/j.cnki.651094.2016.04.006
  中图分类号： O157.5
- 纸质出版：2016
- 稿件说明：
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[1]热西旦·湖加.关于直积图的坚韧度和边坚韧度的注记（英文）[J].新疆大学学报(自然科学版),2016,33(04):407-410.
[1]热西旦·湖加.关于直积图的坚韧度和边坚韧度的注记（英文）[J].新疆大学学报(自然科学版),2016,33(04):407-410. DOI： 10.13568/j.cnki.651094.2016.04.006.

DOI：10.13568/j.cnki.651094.2016.04.006.

摘要

图G的坚韧度t(G)定义为:对非完全图是t(G)=min{|S|/ω(G-S)|SV(G)

ω(G-S)≥2}

而对完全图是∞

其中ω(G-S)表示G-S的连通分支数.边坚韧度定义为t′(G)=min{|X|/ω(G-X)-1|X是G的边割集}.在本文中

我们给出了完全图和圈的直积图的坚韧度

并且提供了完全图和正则图类的直积图的边坚韧度公式.

Abstract

The toughness t(G) of a noncomplete graph G is defined as t(G) = min{|S|/ω(G-S) | S(?) V(G)

ω(G-S) > 2}and the toughness of a complete graph is ∞

where ω(G- S) is

the number of connected components of G- S.The edge-toughness t′(G) of G is defined as t'(G) = min{(|X|)/(ω(G-X)-1) X is an edge-cut set of G}.In this paper

we determine the toughness of Kronecker product of a complete graph and a cycle

and supply formulae for the edge-toughness of Kronecker product of a complete graph and regular graphs.

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references

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