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Questions about graphs, discrete structures of nodes which are connected by edges, including trees and graphs with weighted edges.

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Count of all simple paths between two vertices in a Complete graph

$c(1)=0,$ $c(n)=(n-2)*c(n-1)+1$ suppose we have c(n-1) path in (n-1)-Complete Graph. when we add one more vertices, we add $(n-2)*c(n-1)$ new path and one for directed path. the result is same as r …
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  • 131
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Count of all simple paths between two vertices in a Complete graph [closed]

A path is simple if no vertices are repeated. How many simple paths exist between two vertices in a complete graph? One way is listing all simple paths using depth-first search. but I think it should …
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  • 131