C3r-圈单路图Q-谱半径的极限和上界

The Limit and the Upper Bound for Q-spectral Radius of C3r-cycle Single Path-graphs

设Pn=v1v2…vn表示n阶路,Cr3表示有一个公共顶点的r个三角形,该公共顶点称为Cr3的中心。Cr3-圈单路图Gn,Cr3表示用一边连接Cr3的中心和Pn的端点vn后得到的图(见图1)。文章研究Q-谱半径q(Gn,Cr3)(r≥2,r∈Z)的上界,并且证明了q(Gn,Cr3)收敛到它的Q-谱半径的上界。

LetPn=v1v2…vnbe a path of order n.,C r3 be r triangles with a common vertex which is called its center,Gn,C r3is obtained by connecting the center of C r3with vn end of Pn（see Fig1）.In this paper,we investigate the upper bounds for the Q-spectral radius q（Gn,Cr3）,where r is a positive integer.Furthermore,we prove that q（Gn,Cr3）are quickly convergence to the upper bounds of its Q-spectral radius.