定向图的斜Randic能量  

Skew Randic energy of an oriented graph

作　　者：郭立峰[1] 王力工[1] 

机构地区：[1]西北工业大学理学院应用数学系,西安710072

出　　处：《运筹学学报》2016年第4期77-84,共8页Operations Research Transactions

基　　金：国家自然科学基金(No.11171273)

摘　　要：图G是一个简单无向图,G~σ是图G在定向σ下的定向图,G被称作G~σ的基础图.定向图G~σ的斜Randi6矩阵是实对称n×n矩阵R_s(G~σ)=[(r_s)_(ij)].如果(v_i,v_j)是G~σ的弧,那么(r_s)_(ij)=(d_id_j)^(-1/2)且(r_s)_(ji)=(d_id_j)^(-1/2),否则(r_s)_(ij)=(r_s)_(ji)=0.定向图G~σ的斜Randi能量RE_s(G~σ)是指R_s(G~σ)的所有特征值的绝对值的和.首先刻画了定向图G~σ的斜Randi矩阵R_s(G~σ)的特征多项式的系数.然后给出了定向图G~σ的斜Randi能量RE_s(G~σ)的积分表达式.之后给出了RE_s(G~σ)的上界.最后计算了定向圈的斜Randi能量RE_s(G~σ).Let G be a simple undirected graph and Gσ the corresponding oriented graph of G with the orientation a. G is said to be the underlying graph of Ga. The skew Randic matrix of an oriented graph Gσ is the real symmetric matrix R_s（G-σ）=[（r_s）_（ij）], where （R_s（G-σ）=[（r_s）_（ij）] and （rs）ji = -（dido）- if （v,v） is an arc of a, otherwise （r_s）_（ij）=（r_s）_（ji）=0 The skew Randid energy RE（Gσ） of Gσ is the sum of absolute values of the eigenvalues of Rs（Gσ）. In this paper, we firstly characterize the coefficients of the characteristic polynomial of Rs（Gσ）. Secondly we give an integral representation for the skew Randid energy of Gσ. Thirdly we show a new upper bound of RE（Gσ）. Finally we compute Res（Gσ） of oriented cycles.

关 键 词：斜Randi矩阵 斜Randi能量 

分 类 号：O157.5[理学—数学]