中文摘要：

Nikiforov等人最近将图谱研究与极值图论相结合,提出了谱Turán型问题：给定一个图F,设G是一个不含子图与F同构的n阶图,那么图G的谱半径至多是多少？双圈图是边数等于顶点数加1的简单连通图。近期,部分学者对双圈图的谱半径进行了研究,确定了双圈图谱半径的第1-10大值和相应的极图。受此启发,研究了不含三圈的双圈图,确定不含三圈的双圈图的谱半径的上界,并刻画了相应的极图。

英文摘要：

Reeently, Nikiforov et al. , combining spectral graph theory with the extremal graph theory, proposed the spectral Turun problem ： ＂Given a graph F, what is the maximum spectral radius of a graph of order n, with no subgraph isomorphic to F？＂ When the F is complete graph, path, and cycle etc, they determine the maximum spectral radius of the graph G respectively. A bicyclic graph is a connected graph in which the number of edges equals the number of vertices plus 1. Its spectra has been investigated widely. Inspired by the above problems, in this paper we investigate the spectral radius of triangle - free bicyclic graphs, determine the largest spectral radius together with the corresponding extremal graph among all triangle - free bicyclic graphs of order, n（n≥8）