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liberstina [14]
2 years ago
12

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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Step-by-step explanation:

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3 years ago
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12+root of 35 divided by 2 + 12-2 root of 35 divided by 2
nadya68 [22]
So : 12+ \frac{\sqrt{35}}{2} + \frac{12-2 \sqrt{35} }{2}?

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Add like terms -- 12 +24 = 36       \sqrt{35}-2 \sqrt{35} = \sqrt{35}

Now we are at \frac{24+ \sqrt{35} }{2} Which is the lowest possible simplified version while remaining at exact value. 

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3 years ago
carols bikes 1 kilometer east 4 kilometers north and then 5 kilometers east again. how far is caroll from her starting position
Volgvan
That'd be a total of 6 km east and 4 km north.

The distance traveled from Carol's starting point, along the path described, is
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