循环图的Kirchhoff指标  

The Kirchhoff index of circulant graphs

作　　者：周后卿[1] 周琪[2] 

机构地区：[1]邵阳学院数学系,湖南邵阳422004 [2]湖南农业大学经济学院,长沙410128

出　　处：《华中师范大学学报（自然科学版）》2014年第2期162-167,共6页Journal of Central China Normal University：Natural Sciences

基　　金：湖南省自然科学基金项目(13JJ3118)

摘　　要：图G的Kirchhoff指标定义为G中所有点对之间的电阻距离之和,记为Kf(G).图G为循环图,如果图G的邻接矩阵是循环矩阵;图G为整谱图,若它的特征值全为整数.该文利用循环图的Laplacian谱,讨论了循环图的Kirchhoff指标下界;借助Ramanujan和,利用Euler函数和Mobius函数,得到了一个关于整循环图的Kirchhoff指标的简便计算公式.这样无须求出整循环图的特征值,也可求整循环图的Kirchhoff指标.The Kirchhoff index,Kf（G）,is the sum of resistance distances between all pairs of vertices in G.A graph G is called circulant graph if it has a circulant adjacency matrix.A graph G is called an integral graph if it has an integral spectrum.In this paper,using Laplacian spectrum of circulant graphs,we discuss and give a new lower bound for the Kirchhoff index.According to Ramanujan sums,applying the Euler function and the Mobius function,we obtain a simple formula for the Kirchhoff index of integral circulant graphs.Then we can calculate the Kirchhoff index,and we do not calculate its eigenvalues.

关 键 词：循环图 整循环图 LAPLACIAN特征值 KIRCHHOFF指标 

分 类 号：O157.5[理学—数学]