Cycle Spaces of Digraphs

Chris Godsil; Krystal Guo

Cycle Spaces of Digraphs

Combinatorics 2016-09-30 v1

Authors: Chris Godsil , Krystal Guo

Abstract

The cycle space of a graph corresponds to the kernel of an incidence matrix. We investigate an analogous subspace for digraphs. In the case of digraphs of graphs, where every edge is replaced by two oppositely directed arcs, we give a combinatorial description of a basis of such a space. We are motivated by a connection to the transition matrices of discrete-time quantum walks.

Keywords

dynamical systems graph cycles graph theory

Cite

@article{arxiv.1609.09118,
  title  = {Cycle Spaces of Digraphs},
  author = {Chris Godsil and Krystal Guo},
  journal= {arXiv preprint arXiv:1609.09118},
  year   = {2016}
}