Properties of adjacency matrix of the directed cyclic friendship graph.

Abundance of information about the structure of a graph can be derived from the eigenvalues of its matrix representation. The eigenvalues are always connected to the characteristic polynomial of the matrix representation of a graph. In this paper, we discuss about the properties of adjacency matrix of the directed cyclic friendship graph, its cycle part is clockwise-oriented. By adding the values of the determinants of all directed cyclic induced subgraphs, the coefficients of the characteristic polynomial of the adjacency matrix of the directed cyclic friendship graph can be obtained. The real eigenvalues are obtained by factorization method, while the complex eigenvalues are obtained by root of complex number formula. [ABSTRACT FROM AUTHOR]