围长给定双圈图的A_(α)-谱半径的上界

An Upper Bound on the A_(α)‑spectral Radius of Bicyclic Graphs with a Given Girth

图的A_(α)-矩阵是图的度对角矩阵和邻接矩阵的凸线性组合,是图的邻接矩阵和无符号拉普拉斯矩阵的共同推广,其最大特征值称为图的A_(α)-谱半径。对于α∈[1/2,1),本文确定了围长给定的n阶双圈图的A_(α)-谱半径的上界和极图,推广了已有的成果。

The Aα‐matrix of a graph is the convex linear combinations of the diagonal matrix and the adjacency matrix,which can be regarded as a common generalization of the adjacency matrix and the signless Laplacian matrix.Its maximum eigenvalue is called the Aα‐spectral radius of the graph.Forα∈[1/2,1),in this paper,the upper bound and polar graph of the Aα-spectral radius of n-order bicyclic graphs with given girth are determined,which generalizes the existing results.