轮图的平衡性  

The Balanced Wheel Graph

作　　者：李诗雅 马晓玢 LI Shi-ya;MA Xiao-bin(School of Mathmatics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《长春师范大学学报》2022年第12期15-19,共5页Journal of Changchun Normal University

基　　金：国家自然科学基金项目“基于典型群的交换图和零因子图的自同构群及自同态正则性”(12001010);中国博士后科学基金项目“关于零因子图的代数与组合结构的研究”(2019M662131)。

摘　　要：基于简单图中正、负惯性指数以及秩与符号差的关系,运用矩阵等价变化的方法求得轮图W_(n)在阶数不同条件下的秩,并根据轮图W n邻接矩阵的正、负惯性指数之和等于秩的关系,通过删除轮图W_(n)中度数最大的顶点的方法求出符号差的取值范围,同时刻画了轮图W_(n)在阶数n不同条件下的平衡性,得到当且仅当n=1(mod 4)时,轮图W_(n)是平衡的结论.Based on positive and negative inertia indices and the relationship between rank and signature in the simple graph,this paper obtains the rank of the wheel graph W n under different orders by using the matrix equivalent change method,and according to the relationship that the sum of the positive and negative inertia exponents of the adjacency matrix of the wheel graph W n is equal to the rank.The value range of signature is obtained by deleting the vertex with the largest degree in wheel graph W_(n),and the balance of the wheel graph W_(n )under different order n is described.It is obtained that the wheel graph W_(n) is balanced if and only if n=1(mod 4).

关 键 词：符号差 轮图 平衡性 

分 类 号：O157.5[理学—数学]