几类特殊图的ABC能量  

The ABC energies of several classes of special graphs

作　　者：刘海琴 邵燕灵[3] LIU Haiqin;SHAO Yanling(The Ministry of Basic, Shanxi Agricultural University, Taigu 030801, Shanxi, China;College of Big Data, North University of China, Taiyuan 030051, China;School of Science, North University of China, Taiyuan 030051, China)

机构地区：[1]山西农业大学基础部,山西太谷030801 [2]中北大学大数据学院,太原030051 [3]中北大学理学院,太原030051

出　　处：《华中师范大学学报（自然科学版）》2022年第3期401-406,412,共7页Journal of Central China Normal University：Natural Sciences

基　　金：山西省青年科技研究基金项目(201801D221013);山西农业大学科技创新基金项目(2014010).

摘　　要：图G的ABC能量定义为图G的ABC矩阵的n个特征值的绝对值之和,记为E_(ABC)(G)=ni=1|λ_(i)|.该文利用图的ABC能量的定义和性质,结合几类特殊图的结构,分析了路图、星图、完全图、完全二部图、友谊图以及风车图的ABC特征多项式,给出了ABC能量,并给出了路图、星图、完全图分别删去一条边后其ABC能量的变化趋势.The ABC energy of G is the sum of absolute values of the eigenvalues of ABC(G),that is E_(ABC)(G)=ni=1|λ_(i)|.In this paper,the ABC characteristic polynomials of P_(n)、S_(n)、K_(n)、K_(m,n)、F_(n)、D^(4)_(n) are analyzed by using the definition and properties of ABC energy of graphs and combining the structures of several special graphs.The corresponding ABC energy is given,and the change trend of ABC energy of P_(n)、S_(n)、K_(n) after deleting an edge is given.

关 键 词：简单图 ABC特征多项式 ABC能量 

分 类 号：O157[理学—数学]