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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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PLEASE HELP! <br><br> i’ll mark brainliest if you’re correct!

Jobisdone [24]

Answer:

y = 5

Step-by-step explanation:

Since this is an isosceles triangle, Angle B and Angle C are equivalent. We can use this to find x

3x = 75

x = 25

Angles in a triangle add up to 180, so knowing the measure of Angle B and Angle C, we can find the measure of Angle A

Angle A = 180-(75+75)

Angle A = 180-150

Angle A = 30

We know Angle A = 4y+10

4y + 10 = 30

4y = 20

y = 5

6 0

2 years ago

A triangle has interior angles measuring 36° and 112°. Which triangles are similar to this triangle? Select True or False for ea

morpeh [17]

Hi there!

Since the interior measures of triangles added up always equals 180 degrees, the other interior angle of the triangle must be 32 degrees.

180 - 112 - 36 = 32

So, any triangle with interior measures that measure any angles of 36, 112, and 32 degrees are similar.

<span>triangle with interior angles measuring 36° and 32° - true
triangle with interior angles measuring 36° and 148° - false
triangle with interior angles measuring 32° and 112° - true
triangle with interior angles measuring 112° and 148 - </span>false

Hope this helps!

3 0

4 years ago

Read 2 more answers

Christine took 3 tests and had an average of 76. She has one more test to take and she wants an average of 80. What is the lowes

amm1812

Answer: She has to score a minimum of 92 marks to take her average to 80

Step-by-step explanation:

Let the equation be

Three months total = 76 x 3 = 228

(x + 228) / 4 = 80

x + 228 = 80 x 4

x = 320 - 228

x = 92

6 0

3 years ago

45 mi/h = how many ft/s

Inga [223]

237,600 ft is 45 miles

4 0

4 years ago

A function ___ is an expression that defines a function.

laila [671]

Answer:

Option B - Rule) is your answer

7 0

3 years ago