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2 years ago

Is it possible for a simple, connected graph that has n vertices all of different degrees? Explain why or why not.

Mathematics

1 answer:

ryzh [129]2 years ago

8 0

Answer:

It isn't possible.

Step-by-step explanation:

Let G be a graph with n vertices. There are n possible degrees: 0,1,...,n-1.

Observe that a graph can not contain a vertice with degree n-1 and a vertice with degree 0 because if one of the vertices has degree n-1 means that this vertice is adjacent to all others vertices, then the other vertices has at least degree 1.

Then there are n vertices and n-1 possible degrees. By the pigeon principle there are two vertices that have the same degree.

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dusya [7]

Answer:

B - x=5

Step-by-step explanation:

If y=25 is 250% more than y=10, so multiply 2 by 250% and you get 5

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2 years ago

The front and back covers of a text book are each 0.3 thick between the cover are 200 sheets of paper each 0.008 cm thick how hi

shepuryov [24]

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2 years ago

21. 6m – 2n+ 7 Terms: Coefficients: Constants:

harkovskaia [24]

Answer:

Terms: 6m , -2n, 7

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Step-by-step explanation:

terms are the parts of the expression so 6m, -2n and 7

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3 years ago

Ken started a savings account for school. He plans on spending 10% of the money he earns for leisure activities. He needs to hav

KiRa [710]

Answer:

He must earn $2,400 to cover both leisure and $2,160 for school expenses.

Step-by-step explanation:

Let the total amount Ken must earn be k. Then 10% of that would cover leisure activities and the remaining 90% specifically for school expenses.

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3 years ago

Find the distance BF for the points B(1,-1) and F(-3,5)

Nadusha1986 [10]

Use the distance formula:
 $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Plug in the given coordinates:
 $\sqrt{(-3-1)^2 + (5-(-1))^2}$

Simplify:
 $\sqrt{(-3-1)^2 + (5+1))^2}$

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$\sqrt{16+36}$

$\sqrt{52}$
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3 years ago