The Angles and Main Angles of Some Special Graphs

The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of the graph. Let the vector ej =(0, … , 1, … , 0)T and the all -1 vector j =(1, 1, …,1)T, the cosine of the (acute) angle formed by the vector ej and the eigensubspace is called an angle of the graph. The cosine of the (acute) angle formed by the vector j and the eigensubspace is called a main angle of the graph. The angles and main angles are all important parameters on the graph, and they can be combined with the eigenvalues of the graph to determine the degree sequence of the graph, the number of triangles, quadrilaterals and pentagons on the graph, and the characteristic polynomials of the complement graph, but there is little study on the angles and main angles of the graph. In this paper, we determine the angles and main angles of the complete graph, the cube graph, the Petersen graph, the cycle and the complete bipartite graph.

图C_(n)的angle矩阵和main angle矩阵及图C_(n)oC_(m)的谱

一个图的谱定义为它的邻接矩阵的所有特征值的集合。本文假定C_(n)和圈C_(m)为不相交的两个圈,构造新图coronaC_(n)oC_(m),应用矩阵分块和Kronecker矩阵乘法运算得到其谱。同时计算出圈C_(n)的angle矩阵B(C_(n))和main angle矩阵b(C_(n))。