TITLE:
The Angles and Main Angles of Some Special Graphs
AUTHORS:
Haicheng Ma, Shang Gao
KEYWORDS:
Adjacency Matrix, Eigenvalue, Angle, Main Angle
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.6,
June
16,
2020
ABSTRACT: 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.