Stack Exchange Network
Stack Exchange network consists of 181 Q&A communities including
Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Visit Stack Exchange
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this community
Anybody can ask a question
The best answers are voted up and rise to the top
9 years, 6 months ago
A graph with 21 edges has seven vertices of degree 1, three of degree 2, seven of degree 3 and the rest of degree 4. How many vertices does it have?
Dec 1, 2013 at 2:07
107 1 1 gold badge 1 1 silver badge 4 4 bronze badges
The sum of the degrees is twice the number of edges, so just solve for $x$,
$$7\cdot 1 + 3 \cdot 2 + 7 \cdot 3 + x \cdot 4 = 2 \cdot 21$$
Then $7 + 3 + 7 + x$ is the number of vertices.
Dec 1, 2013 at 2:11
3,908 2 2 gold badges 22 22 silver badges 30 30 bronze badges
Suppose that it has $n$ vertices of degree $4$; then the sum of the degrees is $$7+3\cdot2+7\cdot3+4n=4n+34\;.$$ On the other hand, you know that the sum of the degrees of the vertices is twice the number of edges, so ... ?
Dec 1, 2013 at 2:10
Brian M. Scott Brian M. Scott
604k 56 56 gold badges 745 745 silver badges 1230 1230 bronze badges
Sum of degrees is equal to 2times the number of edges.
So we are given the edges as 21 therefore 21*2=42.
So we just solve for y
7*1+3*2+7*3+y*4 = 42
Solving for y=
Therefore 2 is the number of vertices of degree 4
Mar 29, 2019 at 11:23
log in to answer this question.
Not the answer you're looking for? Browse other questions tagged
By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our
Accept all cookies
Necessary cookies only