双圈图的Laplacian谱展

The Laplacian Spread of Bicyclic Graphs

设G是一个简单连通图,矩阵L(G)=D(G)-A(G)称为图的Laplacian矩阵,其中D(G)是图的度对角线矩阵,A(G)是G的邻接矩阵.连通图G的Laplacian谱展是图的最大特征值与次小特征值之差.边数等于顶点数加1的连通图叫做双圈图.研究了双圈图的Laplacian谱展,并确定了具有最大Laplacian谱展的双圈图.

Let G be a simple connected graph.The matrix L（G）=D（G）-A（G） is called the Laplacian matrix of G,where D（G） is the degree diagonal matrix while A（G） is the adjacency matrix of G.The Laplacian spread of a connected graph G is the difference between the largest and second smallest eigenvalue of L（G）.A connected graph is bicyclic if its size equals to its order plus one.The Laplacian spread of bicyclic graphs is studied and the extremal graphs with the maximal Laplacian spread are determined.