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

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

2003-09-05

arxiv.org/abs/math/0309092v2

Discrete Applied Mathematics, Volume 154, Issue 12, 15 July 2006, Pages 1763-1765

Mathematics

Combinatorics

5 pages

Scientific paper

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.

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