Relations between connected and self-avoiding walks in a digraph
نویسندگان
چکیده
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 selfavoiding hikes of length ` from one vertex to another.
منابع مشابه
On relations between connected and self-avoiding walks on a graph
The characterization of a graph via the variable adjacency matrix enables to de ne 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 ...
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