Connectivity in Directed and Undirected Graphs]
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![2. [Connectivity in Directed and Undirected Graphs]: Assume that all the graphs in the fol-
lowing problems are simple, with no self-loops or multiple edges (in the same direction) between any
two vertices.
(a)
Show that the total number of edges for a connected undirected graph with n vertices
is bounded between n - 1 and (2), i.c.,
(b)
n-1<m<
n
Show that the total number of edges for a strongly connected directed graph with n
vertices is bounded between n and n(n − 1). (Hint: If we remove the directions, n-1 suffices.
Why having n - 1 edges isn't sufficient to ensure strong connectivity in a directed graph?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32e88e4b-79b3-499a-bf2c-e1e6d76ab517%2F119bcd3d-fd95-4cce-8315-163bef5c05ec%2Fcvmk4av_processed.png&w=3840&q=75)
Transcribed Image Text:2. [Connectivity in Directed and Undirected Graphs]: Assume that all the graphs in the fol-
lowing problems are simple, with no self-loops or multiple edges (in the same direction) between any
two vertices.
(a)
Show that the total number of edges for a connected undirected graph with n vertices
is bounded between n - 1 and (2), i.c.,
(b)
n-1<m<
n
Show that the total number of edges for a strongly connected directed graph with n
vertices is bounded between n and n(n − 1). (Hint: If we remove the directions, n-1 suffices.
Why having n - 1 edges isn't sufficient to ensure strong connectivity in a directed graph?)
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