距离无符号拉普拉斯整谱的完全r-部图（英文）

Distance Signless Laplacian Integral Complete R-partite Graphs

对一个n个顶点的图G,G的距离无符号拉普拉斯矩阵记为D^Q(G)=Tr(G)+D(G),其中Tr(G),D(G)分别表示G的顶点传输矩阵及其距离矩阵.G的距离无符号拉普拉斯特征多项式(或简称D^Q-多项式)是DQ/G(λ)=|λI_n-D^Q(G)|,其中I_n是n×n阶单位矩阵.如果G的所有D^Q-特征值都是整数,称图G是距离无符号拉普拉斯整谱图.本文将给出完全r-部图是距离无符号拉普拉斯整谱图的一个必要充分条件,从而构造出无穷多类新的距离无符号拉普拉斯整谱图.

For a graph G of order n,the distance signless Laplacian matrix of G is defined as DQ（G）=Tr（G）＋D（G）,where Tr（G） is the diagonal matrix of vertex transmission of G and D（G） is its distance matrix.The distance signless Laplacian characteristic polynomial（or DQ-polynomial） of G is DGQ（λ）=｜λI_n-DQ（G）｜,where I_n is the n×n identity matrix.A graph G is said to be distance signless Laplacian integral if all its DQ-eigenvalues of G are integers.Throughout this paper,we give a necessary and sufficient condition for complete r-partite graphs to be distance signless Laplacian integral,from which we construct infinitely many new classes of distance signless Laplacian integral graphs.