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

Simone Severini

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arXiv · math/0309092

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

Simone Severini

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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.

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Simone Severini. 2006-07-15. On the structure of the adjacency matrix of the line digraph of a regular digraph. https://arxiv.org/abs/math/0309092

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