图经广义并接运算后的(无符号拉普拉斯)特征值的一些结论（英文）

Some Results on the(Signless Laplacian)Eigenvalues of Graphs Obtained by a Generalization of the Join Graph Operation

设G是一个顶点集为{u_1,u_2,…,u_n}的点标号图,H_1,H_2,…,H_n是n个顶点不交的图,将图G中的顶点u_i(i=1,2,…,n)用图H_i代替,若点u_i与点u_j在G中相邻,则连接H_i与H_j中的所有的点,这样得到的图定义为G[H_1,H_2,…,H_n].本文确定了图G[H_1,H_2,…,H_n]的Q-特征多项式和A-特征多项式.最后,作为应用,构造了很多对(无符号拉普拉斯)-同谱图,并给出了一些关于特殊图类的Q-特征值和A-特征值的不等式序列.

If G is labeled and has n vertices u1,u2,…,un, then the graph G[H1,H2,…,Hn] is formed by taking the disjoint graphs H1,H2,…,Hn and then joining every vertex of Hi to every vertex of Hj when ui is adjacent to uj in G. In this paper, we determine the Q-polynomial and A-polynomial of the graph G[H1,H2,…,Hn]. Finally, as an application of these results, we construct many pairs of nonisomorphic （signless Laplacian） cospectral graphs and give some interesting inequality sequences on Q-eigenvalues and A-eigenvalues of particular graphs.