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3 years ago

Let G be a connnectde graph with n vertices and m edges. supposed also that m = n. prove that G contains exactly one cycle

Mathematics

1 answer:

ElenaW [278]3 years ago

7 0

Answer:

Contradiction

Step-by-step explanation:

Suppose that G has more than one cycle and let C be one of the cycles of G, if we remove one of the edges of C from G, then by our supposition the new graph G' would have a cycle. However, the number of edges of G' is equal to m-1=n-1 and G' has the same vertices of G, which means that n is the number of vertices of G. Therefore, the number of edges of G' is equal to the number of vertices of G' minus 1, which tells us that G' is a tree (it has no cycles), and so we get a contradiction.

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3 years ago

Given the set of ordered pairs: {(1,3), (2,7), (x,5), (6,4)}.

MrMuchimi

Answer:

Step-by-step explanation:

2 is a value of x that would not make the set a function because a function can't have multiple coordinates wit hthe same domain (x-coordinate). 2 is a domain that has already been used in the point (2,7). If this is used in (x,5), the point would become (2,5) and repeat a domain.

Note:

The x-coordinate could also be 1 or 6 because they have been used as domains as well.

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