Graph Theory

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Hurlbert's Pebbling Page. Forcing (mathematics) Forcing is equivalent to the method of Boolean-valued models, which some feel is conceptually more natural and intuitive, but usually much more difficult to apply. identify with , and then introduce an expanded membership relation involving the "new" sets of the form .

Forcing (mathematics)

Forcing is a more elaborate version of this idea, reducing the expansion to the existence of one new set, and allowing for fine control over the properties of the expanded universe. Cohen's original technique, now called ramified forcing, is slightly different from the unramified forcing expounded here. A forcing poset is an ordered triple, (P, ≤, 1), where ≤ is a preorder on P that satisfies following splitting condition: For all p ∈ P, there are q, r ∈ P such that q, r ≤ p with no s ∈ P such that s ≤ q, r The largest element of P is 1, that is, p ≤ 1 for all p ∈ P. There are various conventions in use. Associated with a forcing poset P is the class V(P) of P-names.

Using transfinite recursion, one defines val(xˇ, G) = x. so that. Change in the average geodesic distance of a graph when flipping a single edge. Is there a way to determine how the average geodesic distance between nodes of a graph will change just by flipping (1) a single edge without having to traverse the whole graph like in the Djikstra algorithm?

Change in the average geodesic distance of a graph when flipping a single edge

I'm currently doing this by expensively copying the graph, changing the edge, and then calculating the average geodesic distance of the new graph (using Dijkstra's algorithm) and subtracting it from the average geodesic distance of the original graph.. Is there a more clever way to to this? Notes: (1) By flipping a edge I mean the following operation: add the edge if it's absent and remove it if it's present. (2) Good approximations are welcomed. Cesar A. Hidalgo, Homepage.