Strongly Connected Directed Graph - Cuardach Físeáin

. Show that a directed graph is strongly connected if, and only... | Filo

. Show that a directed graph is strongly connected if, and only... | Filo

Undirected vs. directed connectivity. (a) Prove that in any connected undirected graph G=(V, E) there is a vertex v ∈V whose removal leaves G connected. (Hint: Consider the DFS search tree for G . ) (b) Give an example of a strongly connected directed graph G=(V, E) such that, for every v ∈V, removing v from G leaves a directed graph that is not strongly connected. (c) In an undirected graph with 2 connected components it is always possible to make the graph connected by adding only one edge. Gi

Undirected vs. directed connectivity. (a) Prove that in any connected undir…

Kosaraju's Algorithm - Strongly Connected Components

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2. (5 points) Let G be a directed graph represented using an adjacency list. So, each node G[i] has a list of all nodes reachable in 1 step from i (all out-neighbors of i). Suppose each node of G also has a value: e.g., node 1 might have value 100, node 2 might have value50, etc. Give an O(|E| |V| log |V|) time algorithm that computes, for every node, the highest value reachable from that node (i.e., that you can get to by some path from that node). For instance, if it is possible to get to an

2. (5 points) Let G be a directed graph represented using an adjacency list. …

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