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Pré-Publication, Document De Travail Année : 2015

On relations between connected and self-avoiding walks on a graph

Résumé

The characterization of a graph via the variable adjacency matrix enables one to dene a partially ordered relation on the walks. Studying the incidence algebra on this poset reveals unsuspected relations between connected and self-avoiding walks on the graph. These relations are derived by considering truncated versions of the characteristic polynomial of variable adjacency matrix, resulting in a collection of matrices whose entries enumerate the self-avoiding walks of length from one vertex to another.
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Dates et versions

hal-01153191 , version 1 (19-05-2015)
hal-01153191 , version 2 (21-12-2015)

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Thibault Espinasse, Paul Rochet. On relations between connected and self-avoiding walks on a graph. 2015. ⟨hal-01153191v1⟩
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