On the structure of the adjacency matrix of the line digraph of a regular digraph

We show that the adjacency matrix M of the line digraph of a d-regular digraph D on n vertices can be written as M = AB, where the matrix A is the Kronecker product of the all-ones matrix of dimension d with the identity matrix of dimension n and the matrix B is the direct sum of the adjacency matrices of the factors in a dicycle factorization of D.

• Type: Journal
• Year: 2006
• Where: DAM
• Authors: Simone Severini
• Keywords: Adjacency Matrix, All-ones Matrix, DAM 2006, Matrix