双圈图补图的距离谱半径

The Distance Spectral Radius of the Complements of Bicyclic Graphs

设图G是一个简单连通图,点v_(i)和v_(j)之间最短路径的长度称为点v_(i)和v_(j)在图G中的距离,记作dG(v_(i),v_(j)).图G的距离矩阵为D(G)=(dG(v_(i),v_(j)))n×n.距离矩阵D(G)特征值的模的最大值称为图G的距离谱半径.在n阶双圈图补图中刻画了距离谱半径最大的极图.

Let G be a simple connected graph.The distance between vertices v_(i) and v_(j) in the graph G,denoted by dG(v_(i),v_(j)),is the length of the shortest path from v_(i) to v_(j),and D(G)=(dG(v_(i),v_(j)))n×n is the distance matrix of G.The distance spectral radius of G is defined as the maximum module of eigenvalues of distance matrix D(G).We characterize the extremal graph among the complements of bicyclic graphs with n-order which maximizes the distance spectral radius.