Relations between connected and self-avoiding walks in a digraph
Combinatorics
2015-12-22 v2
Abstract
Walks in a directed graph can be given a partially ordered structure that extends to possibly unconnected objects, called hikes. Studying the incidence algebra on this poset reveals unsuspected relations between walks and self-avoiding hikes. These relations are derived by considering truncated versions of the characteristic polynomial of the weighted adjacency matrix, resulting in a collection of matrices whose entries enumerate the self-avoiding hikes of length from one vertex to another.
Cite
@article{arxiv.1505.05725,
title = {Relations between connected and self-avoiding walks in a digraph},
author = {Thibault Espinasse and Paul Rochet},
journal= {arXiv preprint arXiv:1505.05725},
year = {2015}
}