Some Algebraic Properties of n Order Circle Graphs
MO Guiquan
Abstract：In this paper ,we discuss the correlation matrix of n order undirected graph and the correlation matrix of order directed graph , the determinant of adjacency matrix ,the algebraic properties of rank and so on, and get the corresponding conclusion:① the determinant and rank of the correlation matrix M(Cn) of n order undirected graphs are:|M(Cn)|=2,R(M(Cn))=n,n is odd;|M(Cn)|=0, R(M(Cn))=n-1, n is even.②The determinant and rank of the correlation matrix M(Cn) of n order di-rected graph are:|M(Cn)|=0,R(M(Cn))=n-1,n is integer.③The determinant and rank of the adja-cency matrix A(Cn) of the directed graph are:|A(Cn)|=1,R(A(Cn)=n,n is odd; |A(Cn)|=-1, R(A(Cn))=n,n is even.
Keywords：circle graphincidence matrixadjacency matrixdeterminantrank
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：4( 295-298 )