连通图的最小Laplace谱半径的排序  

The Ordering of the Connected Graphs with the Smallest Laplacian Spectral Radii

作　　者：沈利红[1] 邵嘉裕[1] 郭继明[2] 

机构地区：[1]同济大学数学系,上海200092 [2]中国石油大学应用数学系,山东东营257061

出　　处：《数学年刊（A辑）》2008年第2期273-282,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No．10331020)资助的项目．

摘　　要：首先找出了具有最小Laplace谱半径的第2个至第5个n阶单圈图和具有最小Laplace谱半径的n阶双圈图.然后结合有关n阶树的最小Laplace谱半径的排序,给出了所有n阶连通图中Laplace谱半径最小的14个图,当n为偶数时,它们达到了所有n阶连通图中Laplace谱半径最小的9个值(其中有并列的),而当n为奇数时,它们则达到了Laplace谱半径最小的8个值(其中有并列的).This paper first gives the second to the fifth unicyclic graphs of order n with the smallest Laplacian spectral radii and the bicyclic graph of order n with the smallest Laplacian spectral radii. Then by using the ordering of the trees of order n with the smallest Laplacian spectral radii, the authors obtain the first fourteen connected graphs of order n with the smallest Laplacian spectral radii among all the connected graphs of order n, which reach the nine smallest values of the Laplacian spectral radii among all connected graphs of order n when n is even （where some graphs are juxtaposed） and reach the eight smallest values of the Laplacian spectral radii when n is odd （where some graphs are juxtaposed）.

关 键 词：树 单圈图 双圈图 连通图 LAPLACE谱半径 

分 类 号：O157.5[理学—数学]