萤火虫图距离矩阵的两个最大特征值和的下界

令n=2r+2t+s+1(r,s≥1,t≥0),Sn-t是一个n-t阶的星,将S_(n-t)中的r对不同的点分别用r条边连接,在另外的t条悬挂边上分别接上一条边,得到的图叫作萤火虫图.令图G是n个点的萤火虫图,主要确定了图G的距离矩阵D(G)=(d_(ij))_(n×n),距离拉普拉斯矩阵L_D(G)与距离无符号拉普拉斯矩阵Q_D(G)的两个最大特征值和的下界.

The lower bound of sum of two largest eigenvalues of the distance matrix of firefly graph

Let n =2 r+2 t+s+1(r,s≥1,t≥0),and S_(n-t) be a star with n-t vertices.The firefly graph is such a graph that is obtained by connectingr pairs distinct vertices of S_(n-t) withredges,and joiningt edges to the other t distinct pendant vertices of S_(n-t) respectively.Suppose that Gis a firefly graph onnvertices,we determine the lower bounds of the sum of the largest eigenvalue and the second largest eigenvalue of D(G),L_D(G)and Q_D(G)respectively.