中文摘要：

k圈图是边数等于顶点数加k-1的简单连通图．文中确定了不含三圈的k圈图的拟拉普拉斯谱半径的上界，并刻画了达到该上界的极图．此外，文中确定了拟拉普拉斯谱半径排在前五位的不含三圈的单圈图，排在前八位的不合三圈的双圈图．最后说明文中所得结论对不含三圈的k圈图的拉普拉斯谱半径也成立．

英文摘要：

A k-cyclic graph is a connected graph in which the number of edges equals the number of vertices plus k ＋ 1. This paper determines the maximal signless Laplacian spectral radius together with the corresponding extremal graph among all triangle-free k-cyclic graphs of order n. Moreover, this paper gives the first five triangle-free unicyclic graphs on n （n ≥ 8） vertices, and the first eight triangle-free bicyclic graphs on n （n 〉 12） vertices according to the signless Laplacian spectral radius. Finally, the authors of this paper show that the results obtained in this paper also hold for Laplacian spectral radius of triangle-free k-cyclic graphs of order n.