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

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.