Relations between connected and self-avoiding walks in a digraph

Thibault Espinasse (1) , Paul Rochet (2)

1 PSPM - Probabilités, statistique, physique mathématique
2 LMJL - Laboratoire de Mathématiques Jean Leray

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 $\ell$ from one vertex to another.

Mots clés: incidence algebra; directed graph; characteristic polynomial; variable adjacency matrix; poset

Domaines: Combinatoire [math.CO]

Thibault Espinasse, Paul Rochet. Relations between connected and self-avoiding walks in a digraph. 2015. ⟨hal-01153191v2⟩