Q整图新类(英文)

Some new families of Q-integral graphs

对于一个简单图G,方阵Q(G)=D(G)+A(G)称为G的无符号拉普拉斯矩阵,其中D(G)和A(G)分别为G的度对角矩阵和邻接矩阵.一个图是Q整图是指该图的无符号拉普拉斯矩阵的特征值全部为整数.首先通过Stanic得到的六个顶点数目较小的Q整图,构造出了六类具有无穷多个的非正则的Q整图.进而,通过图的笛卡尔积运算得到了很多的Q整图类.最后,得到了一些正则的Q整图.

Let G be a simple graph.The matrix Q（G）= D（G）＋ A（G）denotes the signless Laplacian matrix of G,where D（G）and A（G）denote the diagonal matrix and the adjacency matrix of G respectively.A graph is called Q-integral if its signless Laplacian spectrum consists entirely of integers.In this paper,we firstly construct six infinite classes of nonregular Q-integral graphs from the known six smaller Q-integral graphs identified by Stanic.Furthermore,we obtain large families of Q-integral graphs by the Cartesian product of graphs.Finally,we obtain some regular Q-integral graphs.