依赖于点的度数的一类图的能量下界  

On Graphs Whose Lower Bound for the Energy Depends on the Degree of Vertices

作　　者：刘晓燕[1] 郭大昌[1] 

机构地区：[1]广东工业大学应用数学学院,广东广州510006

出　　处：《广东工业大学学报》2009年第1期17-19,共3页Journal of Guangdong University of Technology

摘　　要：G为n阶简单图,其能量记为E(G),E(G)=sum from i=1 to n︱λi︱ ,其中λ1,λ2,…λn为图G的邻接矩阵的特征值.围绕最大度不大于3的n阶无四圈图,证明了其能量不小于n-1.讨论了一类能量大于阶数的图,并进一步得到一类超能图.Let G be a graph on n vertices, A（G） be the adjacency matrix of G, and λ1,λ2,……λn be the eigenvalues of A（G）. The energy of G is defined as E（G） = ∑i=1^n ｜λi｜, The results show that the energy of quadrangle-free graphs, whose maximal degree is not bigger than 3, is not smaller than n-1. Furthermore, such graphs whose energy exceeds the number of its vertices are studied, and one kind of graphs that are hyperenergetic is obtained.

关 键 词：能量 最大度 圈长 无四圈图 超能图 

分 类 号：O157.6[理学—数学]