具有最小能量的四叶图  

The Four-leaf Graphs with Minimum Energy

作　　者：车雨红[1] 

机构地区：[1]渭南师范学院数理学院,陕西渭南714099

出　　处：《渭南师范学院学报》2016年第4期13-17,共5页Journal of Weinan Normal University

基　　金：陕西省自然科学基金资助项目:拟阵的模糊化与模糊拟阵的优化算法研究(2014JM1026);渭南师范学院理工类科研项目:基于毛毛虫树能量的渭南市能源发展问题研究(15YKP015)

摘　　要：为了探讨具有最小能量值的问题,依据图的能量理论,采用了图解式的方法,研究了n阶四叶图之间的两种能量变换关系,证得当TSk,k≥2时的四叶图具有最小能量的结论。图的能量是图的邻接矩阵的所有特征值的绝对值之和,记为E(G)。如果图中有一块是树,其他块是圈,且所有的圈都粘在这棵树的根节点上,则称图是仙人掌图,记为G,用G(n,r)表示具有r个圈的n阶仙人掌图集。当r=4且每个圈为三角形时,称图为四叶图,记为C43·T。通过计算它们各自的特征多项式的系数,且对其进行比较,找出了具有最小能量的四叶图,并对所得结果进行了验证。In order to discuss issues with least energy,according to the figure of the theory of energy,using the diagram type,the paper studies the two transformation relations between the four-leaf graphs with n vertices and proves that the four-leaf graphs have minimum energy when T  Sk,k ≥ 2. The energy of a graph is defined as the sum of absolute values of eigenvalues of the adjacent matrix,and it can be denoted by E（ G）. G is called cactus graph if a part of G is a tree,others are circles and all circles are connected with the root of the tree. Let G（ n,r） be the set of cactus graph with n vertices and r circles. The four-leaf graph is a cactus graph when r = 4 and every circle is triangle,and it can be denoted by C43·T.By calculating and comparing their respective characteristic polynomial coefficients,it finds out the four leaf graph with the minimum energy; finally,the result is verified.

关 键 词：图的能量 仙人掌图 四叶图 变换关系 

分 类 号：O157.14[理学—数学]