0 like 0 dislike
7 views
What is the faceshaking lemma in graph theory?
in General Maths by Diamond (40.2k points) | 7 views

1 Answer

0 like 0 dislike
Best answer
Theorem

If we have a planar embedding of a connected graph G with s faces $f_1, f_2, ..., f_s$, then
\[
\sum_{i=1}^{s}deg(f_i) = 2| E(G) |
\]

Corollary:
If the connected graph G has a planar embedding with f faces, the average degree of a face in the embedding is
\[
\frac{2|E(G)|}{f}
\]
by Diamond (40.2k points)

Related questions

0 like 0 dislike
1 answer
asked Apr 25 in General Maths by Tedsf Diamond (40.2k points) | 9 views
0 like 0 dislike
1 answer
asked May 17 in General Maths by Tedsf Diamond (40.2k points) | 22 views
0 like 0 dislike
1 answer
asked Apr 25 in General Maths by Tedsf Diamond (40.2k points) | 7 views
0 like 0 dislike
1 answer
asked Apr 25 in General Maths by Tedsf Diamond (40.2k points) | 11 views
0 like 0 dislike
1 answer
asked Aug 10, 2019 in General Maths by Tedsf Diamond (40.2k points) | 19 views
Welcome to MathsGee Skills Question and Answer Bank, a platform, where you can ask study questions and receive answers from other members of the community. Help is always 100% FREE!
MathsGee Q&A is the knowledge-sharing community where millions of students and experts put their heads together to crack their toughest homework questions.

Enter your email address:

Popular Courses

Python For First Timers
Python For Everyone