具有最小距离拉普拉斯谱半径的双圈图（英文）  

The Bicyclic Graph with the Minimum Distance Laplacian Spectral Radius

作　　者：樊丹丹 牛爱红[2] 王国平[2] FAN Dan-dan;NIU Ai-hong;WANG Guo-ping(College of Mathematical and Physical Sciences,Xinjiang Agricultural University,Urumqi 830052;School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830054)

机构地区：[1]新疆农业大学数理学院,乌鲁木齐830052 [2]新疆师范大学数学科学学院,乌鲁木齐830054

出　　处：《工程数学学报》2020年第1期121-130,共10页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11461071)~~

摘　　要：一个连通图的距离拉普拉斯矩阵的最大特征值称为这个图的距离拉普拉斯谱半径.本文中,我们先得到距离拉普拉斯谱半径的一个好的下界,然后利用这个下界确定了单圈图中具有最小距离拉普拉斯谱半径的唯一极图.最后,再次利用这个下界,并结合距离拉普拉斯矩阵的特征多项式确定出了双圈图中具有最小距离拉普拉斯谱半径的极图.The largest eigenvalue of the distance Laplacian matrix of a connected graph G is called the distance Laplacian spectral radius of the graph G.In this paper we obtain a sharp lower bound of distance Laplacian spectral radius,and then using the bound we determine the unique graph which has the minimum distance Laplacian spectral radius among all unicyclic graphs.Finally,by using the bound again as well as the characteristics polynomial of a distance Laplacian matrix,we characterize the unique graph with the minimum distance Laplacian spectral radius among all bicyclic graphs.

关 键 词：距离拉普拉斯谱半径 单圈图 双圈图 

分 类 号：O157.5[理学—数学]