Abstract
AbstractA path system in a graph is a collection of paths with a unique path for every two vertices . We say that is consistent if for any path , every subpath of is also in . It is metrizable if there exists a positive weight function such that is comprised of âshortest paths. We call irreducible if there does not exist a partition such that restricts to a path system on both and . In this paper, we construct an infinite family of nonmetrizable irreducible consistent path systems on certain Paley graphs.
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