中文摘要：

为研究图的无符号拉普拉斯谱半径的界,以图的顶点度di等为参数,通过对图的无符号拉普拉斯矩阵进行相似变换,证明由任意两个图G1和G2得到的广义并接图G的谱半径上确界q（G）.由此刻画达到这个上界的极图当且仅当G1和G2均为正则图.

英文摘要：

To research the bound of the signless Laplacian spectral radius of a graph, taking the vertex degree diand so on of the graph as parameters, by the similarity transformation of the signless Laplacian matrix of the graph, the sharp upper bound q （G） of the signless Laplacian spectral radius of the weak joining graph G is determined, where G is obtained by two random graphs G1 and G2. Based on this, the extremal graph reaching the upper bound is characterized if and only if G1 and G2 are regular graphs.