2. What is the maximal possible number of edges in an undirected graph with n vertices....

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2. What is the maximal possible number of edges in an undirected graph with n vertices....

2. What is the maximal possible number of edges in an undirected graph with n vertices. Explain your answer briefly.

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Answer 1

Answer #1

first node can have a maximum of n-1 edges to other nodes.
second node can have a maximum of n-2 edges to other nodes.
...
last node can have a maximum of 0 edges to other nodes.

total number of edges = 0+1+2+..+(n-2)+(n-1)
= n(n-1)/2

so, total number of edges in a undirected graph is n(n-1)/2

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