一个图G的邻接矩阵A(G)是n×n矩阵,如果vi和vj相邻,那么它的(i,j)位置为1,否则为0.图G的谱半径是邻接矩阵A(G)的最大特征值.本文确定了在所有的树和所有的二部单圈图、二部双圈图、二部三圈图、二部四圈图、二部五圈图以及二部拟树图中所对应的具有最大谱半径的图.
The adjacency matrix A(G) of a graph G is the nxn matrix with its(i,j)-entry equal to 1 if vi and vj are adjacent,and 0 otherwise.The spectral radius of G is the largest eigenvalue of A(G).In this paper we determine the graphs with maximum spectral radius among all trees,and all bipartite unicyclic,bicyclic,tricyclic,tetracyclic,pentacyclic and quasi-tree graphs,respectively.