关于三叶图的能量变换

On Energy Changing of 3-leaves Graphs

图的能量是图的邻接矩阵的特征值的绝对值之和,记为E(G)。用G(n,r)表示为具r个圈的n阶仙人掌图集,当r=3且每个圈为三角形时,称图G为三叶图。主要讨论n阶三叶图之间的能量变换关系。首先得到m(G,k)与b_i(G)的关系;其次得到此类图之间满足变换关系Ⅰ、Ⅱ下的能量关系;并证得当T≌S_k,k≥2时的三叶图具有最小能量。

The energy of a graph is defined as the sum of the absolute value of eigenvalues of the adjacent matrix on the graph. G （ n, r） denotes the set of n order cacti graph with r cycles. When r = 3 and every cycls is triangle, it is called n order 3-leaves graph. In this paper, we mainly study the energy transformation raltion of 3-leaves graphs. Firstly, we get the relation between m （ G, k ） and bi （G）. Secondly, we obtain the energy connection between the graphs which satisfy the transfonntion Ⅰ or Ⅱ. And we get that the 3-leaves graphs have the minimum energy when T≌Sk, k ≥2.