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…
17 Meith 2020
numerade.com
In an undirected graph, the degree d(u) of a vertex u is the number of neighbors u has, or equivalently, the number of edges incident upon it. In a directed graph, we distinguish between the indegree din(u), which is the number of edges into u, and the outdegree dout(u), the number of edges leaving u (a) Show that in an undirected graph, ∑u ∈V d(u)=2|E| (b) Use part (a) to show that in an undirected graph, there must be an even number of vertices whose degree is odd. (c) Does a similar statement
In an undirected graph, the degree d(u) of a vertex u is the number of neighb…
17 Meith 2020
numerade.com
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