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3 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]3 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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3 years ago

A contractor bought 7.6 ft2 of sheet metal. She has used 3.5 ft2 so far and has $123 worth of sheet metal remaining. The equati

Sergio039 [100]

Answer:

Sheet metal remaining = 4.1x

cost per square foot of sheet metal = $30

Step-by-step explanation:

Total sheet metal bought = 7.6 ft2

Total sheet metal used = 3.5 ft2

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7.6x − 3.5x = 123

Where,

x = cost per square foot

7.6x − 3.5x

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2 years ago

What is the y-coordinate of the solution for the system of equations? x−y=−11 y+7=−2x

ICE Princess25 [194]

Answer:

$y= 5$

Step-by-step explanation:

Given the system of equations:

$x-y=-11$

$y+7=-2x$

In order to find the y coordinate of the solution we must first find the solution to this system of equations. We first start by solving one of the given equations and then substitute the answer of that into the second equation and further solve to get the final answers.

$x=y=-11$