1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
cestrela7 [59]
3 years ago
10

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.

You might be interested in
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
Other questions:
  • Kelly found some dimes and pennies in her dad's car . she found 5 coins in all. the coins totaled more than 20 cents, but less t
    14·1 answer
  • Ana helped her mom this weekend. She earned $25. On Monday she purchased snacks for herself and her friends and spent $6.50. On
    13·2 answers
  • On any given day, the number of users, u, that access a certain website can be represented by the inequality 125-4530
    5·1 answer
  • What is the standard form of the equation<br><br>Center (-14,5), circumference: 22π
    14·1 answer
  • Plz help ill mark u brainliest
    7·1 answer
  • an amusement park it's admission price to $15.50 per day, but now charges $1.50 per ride mark has 26 to spend on admission and r
    8·1 answer
  • Lauren divided a pile of paper into 5 stakes. The line plot shows the height of each stack of paper.
    11·1 answer
  • The different between three times a number and five is equal to the product of four times the number increased by two.
    14·1 answer
  • How does the structure of a polynomial help me decide how to factor it?
    10·1 answer
  • A university is comparing the grade point averages of theater majors with the grade point averages of history majors. The univer
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!