A directed graph can be represented by several matrix representations, such as adjacency matrix, in-degree Laplacian matrix, and out-degree Laplacian matrix. A directed cyclic sun graph is a directed graph which is obtained by adding a directed edge and a vertex called the outer vertex as its tail to every vertex in the directed cycle graph. The inner vertices always form a directed cycle graph. The directed edges in the cycle graph is oriented in such a away so that clockwise. In this paper we give the properties of adjacency, in-degree Laplacian, and out-degree Laplacian matrices of directed cyclic sun graph such as characteristic polynomial and eigenvalues. The eigenvalues of the matrices mentioned above can be real or complex numbers.

Topics
Graph theory, Operator theory, Matrix calculus
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2019
Author(s)