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## Homework Statement

1. How many vertices will the following graphs have if they contain:

(a) 12 edges and all vertices of degree 3.

(b) 21 edges, three vertices of degree 4, and the other vertices of degree 3.

(c) 24 edges and all vertices of the same degree.

## Homework Equations

"Theorem 1

In any graph, the sum of the degrees of all vertices is equal to twice the number of

edges."

## The Attempt at a Solution

[/B]

a) 12*2=24

3v=24

v=8

(textbook answer: 12)

b)

21*2=42

3*4 + 3v = 42

12+3v =42

3v=30

v=10

add the other 3 given vertices, and the total number of vertices is 13

(textbook answer: 9)

c) 24*2=48

48 is divisible by 1,2,3,4,6,8,12,16,24,48

Thus those would be the possible answers

(textbook answer: 8 or 10 or 20 or 40.)