摘要:Let G1,G2 be two simple connected graphs.The partially subdivision neighbourhood corona of G1 and G2,denoted by G1-★G2,is obtained by taking one copy of G1 and |V(G1)| copies of G2,and joining the neighbours of the i-th vertex of G1 to every vertex in the i-th copy of G2,then inserting a new vertex into every edge of G1.In this paper,we determine the adjacency spectrum,Laplacian spectrum and signless Laplacian spectrum of G1-★G2 in terms of those of two factor graphs G1 and G2.In addition,as many applications of these results,we consider constructing infinite pairs of adjacency cospectral,Laplacian cospectral and signless Laplacian cospectral graphs.Moreover,we compute the number of spanning trees of G1-★ G2 in terms of the Laplacian spectra of two factor graphs G1 and G2.%设G1,G2是两个简单连通图,图G1,G2的局部剖分邻接冠图G1-★G2是指复制一个G1和|V(C1)|个G2,图G1的第i个点的邻点与复制的第i个图G2的每一个点相连接,然后在G1每一条边上插入一个新的点而得到的图类.本文利用两个图G1,G2的邻接谱、Laplacian谱和无符号Laplacian谱刻画了局部剖分邻接冠图G1-★G2的邻接谱、Laplacian谱和无符号Laplacian谱.另外,本文利用上述结果构造出了若干对邻接同谱图、Laplacian同谱图和无符号Laplacian同谱图.进一步地,本文也利用两个因子图G1,G2的Laplacian谱计算出了局部剖分邻接冠图G1-★G2的生成树数目.