路和圈、圈和圈的Kronecker积图的超点连通性

吴丽芸; 田应智

doi:10.13568/j.cnki.651094.651316.2021.02.17.0001

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路和圈、圈和圈的Kronecker积图的超点连通性

更新时间：2026-01-21

- 路和圈、圈和圈的Kronecker积图的超点连通性
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 39, Issue 2, Pages: 176-181(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.651094.651316.2021.02.17.0001
  CLC： O157.5
- Published：2022
- 稿件说明：
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[1]吴丽芸,田应智.路和圈、圈和圈的Kronecker积图的超点连通性[J].新疆大学学报(自然科学版)(中英文),2022,39(02):176-181.
[1]吴丽芸,田应智.路和圈、圈和圈的Kronecker积图的超点连通性[J].新疆大学学报(自然科学版)(中英文),2022,39(02):176-181. DOI： 10.13568/j.cnki.651094.651316.2021.02.17.0001.

DOI：10.13568/j.cnki.651094.651316.2021.02.17.0001.

摘要

如果图G的每一个最小点割都是某个点的邻点集

那么G是超点连通的

或者简称为是super-κ的.图G1与G2的Kronecker积图是一个点集为V (G1×G2)=V (G1)×V (G2)

边集为E(G1×G2)={(u1

v1)(u2

v2):u_1u2∈E(G1)

v_1v2∈E(G2)}的图.本文证明了对整数m≥4和奇数n≥3

Pm×Cn是超点连通的;对整数m≥5和奇数n≥3

Cm×Cn是超点连通的.

Abstract

A graph G is super connected

or simply super-κ

if every minimum vertex-cut isolates a vertex. The Kronecker product G1 × G2 of graphs G1 and G2 is the graph with vertex set V(G1 × G2) = V(G1) × V(G2) and edge set E(G1 × G2) = {(u1

v1)(u2

v2) : u_1u2 ∈ E(G1)

v_1v2 ∈ E(G2)}. In this paper

we prove that Pm × Cn is super-κ for m ≥ 4

n ≥ 3 and n is odd; Cm × Cn is super-κ for m ≥ 5

n ≥ 3 and n is odd.

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references

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