整可逆图的克罗内克积的逆

doi:10.6040/j.issn.1671-9352.0.2020.344

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (11): 87-92.doi: 10.6040/j.issn.1671-9352.0.2020.344

• • 上一篇

整可逆图的克罗内克积的逆

王霞¹,边红^1*,于海征²

1.新疆师范大学数学科学学院, 新疆乌鲁木齐 830017;2.新疆大学数学与系统科学学院, 新疆乌鲁木齐 830046

发布日期:2021-11-15
作者简介:王霞(1996— ), 女, 硕士研究生, 研究方向为图论及其应用研究. E-mail:1793248404@qq.com*通信作者简介:边红(1974— ), 女, 博士, 教授, 研究方向为图论及其应用研究. E-mail:bh1218@163.com
基金资助:
国家自然科学基金资助项目(11761070,61662079);2021年新疆维吾尔自治区自然基金联合项目(2021D0K078);2022年新疆维吾尔自治区自然基金青年项目;2022年新疆师范大学一流专业一流课程资助项目

Inverse of Kronecker product of integrally invertible graphs

WANG Xia¹, BIAN Hong^1*, YU Hai-zheng²

1. Department of Mathematics, Xinjiang Normal University, Urumqi 830017, Xinjiang, China;
2. Department of Mathematics, Xinjiang University, Urumqi 830046, Xinjiang, China

Published:2021-11-15

摘要/Abstract

摘要： 图G₁和G₂的克罗内克积G₁⊗G₂具有点集V(G₁)⊗V(G₂),在G₁⊗G₂中两个点(u₁,v₁)和(u₂,v₂)相邻当且仅当 u₁u₂∈E(G₁)且 v₁v₂∈E(G₂)。对整可逆图(即图的邻接矩阵的逆矩阵中只包含整数)的克罗内克积的逆进行刻画。

关键词: 逆图, 克罗内克积, 冠图, 完美匹配

Abstract: The Kronecker product G1⊗G2 of graphs G1 and G2 is the graph with the vertex set V(G1)⊗V(G2), two vertices (u1,v1) and (u2,v2) being adjacent in G1⊗G2 if and only if u1u2∈E(G1) and v1v2∈E(G2). The inverse of Kronecker product of integrally invertible graph is characterized.

Key words: inverse graph, Kronecker product, corona graph, perfect matching

中图分类号:

O157.5

王霞,边红,于海征. 整可逆图的克罗内克积的逆[J]. 《山东大学学报(理学版)》, 2021, 56(11): 87-92.

WANG Xia, BIAN Hong, YU Hai-zheng. Inverse of Kronecker product of integrally invertible graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 87-92.

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整可逆图的克罗内克积的逆

Inverse of Kronecker product of integrally invertible graphs

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