A graph with n nodes is connected, undirected, and acyclic. How many edges must it have? (Select ...
A graph with n nodes is connected, undirected, and acyclic. How many edges must it have? (Select the answer from the following options and prove your choice):
a) n
b) n*(n-1)
c) n- 1
d) n/2 - 1
Homework Answers
The correct answer is option c i.e. n-1. The reason behind this is that, a connected undirected graph with n nodes and without any cycle is a tree and a tree over n vertices always has n-1 edges.
Please comment for any clarification.
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A graph with n nodes is connected, undirected, and acyclic. How many edges must it have? (Select ...
Problem 6. In lecture, we saw that an undirected graph with n nodes can have at...
Problem 6. In lecture, we saw that an undirected graph with n nodes can have at most n(n - 1)/2 edges. Such a graph necessarily has one connected component. The greatest number of edges possible in a disconnected graph, however, is smaller. Suppose that G (V, E) is a disconnected graph with n nodes, how large can |El possibly be? You do not need to prove your answer, but you should provide some explanation of how you obtained it.
We now consider undirected graphs. Recall that such a graph is • connected iff for all...
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P9.6.3 Prove that a connected undirected graph G is bipartite if and only if there are no edges between nodes at the same level in any BFS tree for G. (An undirected graph is defined to be bipartite if its nodes can be divided into two sets X and Y such that all edges have one endpoint in X and the other in Y.)
P9.6.3 Prove that a connected undirected graph G is bipartite if and only if there are...
Let G be a connected graph with n vertices and n edges. How many cycles does...
Let G be a connected graph with n vertices and n edges. How many cycles does G have? Explain your answer.
How much work must Kruskal's MST algorithm do before it starts choosing edges for its MST? Assume the undirected graph has n vertices and m edges. Explain the necessary preliminary work and its b...
How much work must Kruskal's MST algorithm do before it starts choosing edges for its MST? Assume the undirected graph has n vertices and m edges. Explain the necessary preliminary work and its big-O cost if done efficiently What are the best case and worst case for Kruskal's MST algorithm with parameters n and/or m? Explain your answer.
How much work must Kruskal's MST algorithm do before it starts choosing edges for its MST? Assume the undirected graph has n...
Define the graph Gn to have the 2n nodes 20, 21,...,an-1, bo, b1, ..., bn-1 and...
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2. What is the maximal possible number of edges in an undirected graph with n vertices. Explain your answer briefly.
Answer all the BLANKS from A to N please. 7. For the graph shown below at...
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P9.6.3 Prove that a connected undirected graph G is bipartite if and only if there are no edges between nodes at the same level in any BFS tree for G. (An undirected graph is defined to be bipartite if its nodes can be divided into two sets X and Y such that all edges have one endpoint in X and the other in Y.)
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How much work must Kruskal's MST algorithm do before it starts choosing edges for its MST? Assume the undirected graph has n vertices and m edges. Explain the necessary preliminary work and its big-O cost if done efficiently What are the best case and worst case for Kruskal's MST algorithm with parameters n and/or m? Explain your answer.
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Define the graph Gn to have the 2n nodes 20, 21,...,an-1, bo, b1, ..., bn-1 and the following edges. Each node ai, for i = 0,1,...,n - 1, is connected to the nodes b; and bk, where j = 2i mod n and k = (2i + 1) mod n (a) Prove that for every n, G, has a perfect matching. (b) How many different perfect matchings does G100 have?
Answer all the BLANKS from A to N please.
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