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

Liu Xiao-yan; Guo Da-chang

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

更新时间：2026-05-27

- On Graphs Whose Lower Bound for the Energy Depends on the Degree of Vertices
- Vol. 26, Issue 1, Pages: 11(2009)
- 作者机构：
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- Online First：01 January 2009，
  
  Published：2009
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刘晓燕, 郭大昌. 依赖于点的度数的一类图的能量下界[J]. 广东工业大学学报, 2009, 26(1): 11.

Liu Xiao-yan, Guo Da-chang. On Graphs Whose Lower Bound for the Energy Depends on the Degree of Vertices[J]. 2009, 26(1): 11.
刘晓燕, 郭大昌. 依赖于点的度数的一类图的能量下界[J]. 广东工业大学学报, 2009, 26(1): 11. DOI：

Liu Xiao-yan, Guo Da-chang. On Graphs Whose Lower Bound for the Energy Depends on the Degree of Vertices[J]. 2009, 26(1): 11. DOI：

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.

Abstract

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)=sum from i=1 to 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. 更多还原

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