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

  • Authors:

  • Simone Severini

  • Affiliations:

  • Department of Computer Science, University of Bristol, Bristol, UK

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2006

Quantified Score

Hi-index 0.04

Visualization

Abstract

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.