行数为2的变换图的若干性质  

Some Properties of Interchange Graph with Row Number Being 2

作　　者：金晶晶[1] JIN Jingjing(College of General Education,Fujian Chuanzheng Communications College,Fuzhou 350007,China)

机构地区：[1]福建船政交通职业学院通识教育学院,福建福州350007

出　　处：《海南师范大学学报（自然科学版）》2022年第2期170-174,共5页Journal of Hainan Normal University（Natural Science）

基　　金：福建省中青年教师教育科研项目(JAT210722)。

摘　　要：著名的图论专家Brualdi于1980年提出了关于变换图G(R,S)直径的Brualdi猜想,但至今仍悬而未决。本文定义行数为2的变换图G(R,S)为G(R^(*),S^(*)),其顶点数为[nr],边数为r(n-r)/2(nr),当r≤n/2时,G(R^(*),S^(*))是二部图,当且仅当n=2;G(R^(*),S^(*))是完全图,当且仅当r=1。根据变换图的性质,结合G(R^(*),S^(*))的最大团结构,对变换图G(1,4)、G(2,4)、G(2,5)和G(2,6)进行了作图。The Brualdi’s Conjecture concerning the diameter of the interchange graph G(R,S)was raised in 1980 by Brualdi,a famous expert of graph theory.However,it still remains open now.In this paper,the interchange graph G(R,S)with row number being 2 is defined as G(R^(*),S^(*)).The vertex number is[nr]and the edge number isr(n-r)/2(nr).G(R^(*),S^(*))(r≤n/2)is bipartite if and only if n=2;G(R^(*),S^(*))(r≤n/2)is a complete graph if and only if r=1.Moreover,according to the properties and the maximum clique structure of G(R^(*),S^(*)),the interchange graph G(1,4)、G(2,4)、G(2,5)、G(2,6)are plotted.

关 键 词：变换图 (0 1)-矩阵 向量 直径 同构 

分 类 号：O157.5[理学—数学]