Enumerating simple paths from connected induced subgraphs
Résumé
We present an exact formula for the ordinary generating series of the simple paths, also called self-avoiding walks, between any two vertices of a graph. Our formula involves a sum over the connected induced subgraphs and remains valid on weighted and directed graphs. An intermediary result of our approach provides a unifying vision that conciliates several concepts used in the literature for counting simple paths. We obtain a relation linking the Hamiltonian paths and cycles of a graph to its connected dominating sets.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...