CAJ | 학술논문

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Stani(c)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.
대우일개간단도G,방진Q(G)=D(G)+A(G)칭위G적무부호랍보랍사구진,기중D(G)화A(G)분별위G적도대각구진화린접구진.일개도시Q정도시지해도적무부호랍보랍사구진적특정치전부위정수.수선통과Stani(c)득도적륙개정점수목교소적Q정도,구조출료륙류구유무궁다개적비정칙적Q정도.진이,통과도적적잡이적운산득도료흔다적Q정도류.최후,득도료일사정칙적Q정도.
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 Stani（c）.Furthermore,we obtain large families of Q-integral graphs by the Cartesian product of graphs.Finally,we obtain some regular Q-integral graphs.