Graph Theory: Pure or Applied?

Click For Summary
Graph theory encompasses both pure and applied mathematics, with its utility depending on individual usage. While some view it primarily as a theoretical discipline focused on proofs, others appreciate its practical applications. The discussion suggests classifying graph theory along a concrete/abstract axis, highlighting its visualizable elements. Its relative independence from other mathematical branches allows beginners to engage with the subject without extensive prior knowledge. Ultimately, graph theory's dual nature and accessibility contribute to its appeal in both theoretical and practical contexts.
andlook
Messages
32
Reaction score
0
Hi

Is graph theory a more pure or applied subject?

I thought it was pure but now I am confusing myself because it has so many applications.

Thanks
 
Mathematics news on Phys.org
It is both a theoretical and applied subject. You will decide how you'll use it. You can construct proofs and/or you can experiment with numerous graphs, their properties and their application. but a theoretical background is a must
 
I'd say pure. When I took graph theory, it was all about proving stuff about graphs (which is far from easy!).
 
I have dabbled in it both for fascination of 'pure' aspects and for some applications.

Would it be useful to classify it not by, or not only by, the pure/applied axis but along the concrete/abstract axis. It no doubt has abstract aspects, but it is often about perfectly 'concretely' visualisable things, whether they are useful or not and they always might be - a bit like 2 and 3D Euclidean geometry. Is that not one nice thing about it - for some of us?

Is not another nice aspect that it is relatively independent of other branches of mathematics, so a beginner can go quite far without a vast mathematical background?
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 76 ·
3
Replies
76
Views
6K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K