具有k个悬挂点的单圈图的A_(α)-谱半径

On the A_(α)-spectral Radius of Unicyclic Graphs with k Pendant Vertices

对于任意的α∈[0,1],Nikiforov提出了矩阵A_(α)(G)=αD(G)+(1-α)A(G),记为图G的A_(α)-矩阵,其中A(G)是G的邻接矩阵,D(G)是G的度对角矩阵.矩阵A_(α)(G)的最大特征值称为图G的A_(α)-谱半径.本文考虑有k个悬挂点的所有单圈图,确定了具有最大A_(α)-谱半径的图.

For any realα∈[0,1],Nikiforov proposed the matrixA_(α)(G)=αD(G)+(1)-αA(G),which is the A_(α)-matrix of a graph G,where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the degrees of G.In this paper,we determine the graph with the largestA_(α)-spectral radius among all unicyclic graphs with k pendant vertices.