若干图的卡氏积的距离谱和距离能量(英文)

G是顶点集为{v_1,v_2,…,v_n}的连通简单图,G_1,G_2,…,G_n是有限图。联并图G[G_1,G_2,…,G_n】是按如下方式在G_1UG_2U…UG_n上加边而成的图:在G_i和G_j之间的任何两个顶点间加边,若v_i和v_j在G中相邻.[7]给出了两个距离正则图的卡氏积的距离谱.本文计算了联并图和距离正则图的卡氏积及两个联并图的卡氏积的距离谱.在此基础之上,我们得到了两个利用联并图与非同谱距离正则等能量图作卡氏积及联并图作卡氏积构造非同谱等距离能量图族的方法.

On the Distance Spectra and Energies of Cartesian Product of Some Graphs

A joined union G[G1,G2 ,…Gn] is a graph obtained from the union of graphs G1,G2,…,Gn, by adding MI edges between Gi and Gj, whenever in G vi and vj are adjacent, where G is a simple connected graph with vertex set {v1,v2,…,vn} and Gj a finite graph for Vj ∈ {1, 2,… , n}（ a joined union might not be distance regular）. In [7] the distance spectrum of the cartesian product of two distance regular graphs was given. In the present paper, we compute distance spectra of Cartesian products of a joined union and a distance regular graph and Cartesian products of two joined unions. Based on these results, two methods for constructing groups of distance noncospectral equienergetic graphs from Cartesian products of joined unions and distance regular noncospectral equienergetic graphs and Cartesian products of joined unions are given.