Graph theory without graphs?

In summary, the conversation discusses the possibility of doing graph theory without using pictorial representations. It is mentioned that the definition of a graph does not mention anything about pictorial graphs and that modern mathematics has a tendency to move away from pictures and focus more on algebra. While it is possible to do graph theory without pictures, it is noted that there has been a recent increase in the use of graphs in mathematics explanations. The question is also posed about whether the individual has experience with graph theory using pictures.
  • #1
tgt
522
2
From the definition of a graph, it dosen't mention anything about a pictorial graph. Things are only dealt with set wise so it is possible to do graph theory without graphs? It would be extremely unnatural though.
 
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  • #2
Yes it is possible to do graph theory without pictures. Modern mathematics has a desire to take things away from pictures and move it into algebra, which is a shame really. Entire textbooks go without a single diagram these days...
 
  • #3
Gib Z said:
Yes it is possible to do graph theory without pictures. Modern mathematics has a desire to take things away from pictures and move it into algebra, which is a shame really. Entire textbooks go without a single diagram these days...

I find it the opposite, I think that modern mathematics is growing more pictorial. Now every single explanation has a graph to go with it, and textbooks usually more graphs than ever, since the theory is more developed, with new aspects on calculus etc.
 
  • #4
Gib Z said:
Yes it is possible to do graph theory without pictures. Modern mathematics has a desire to take things away from pictures and move it into algebra, which is a shame really. Entire textbooks go without a single diagram these days...

Have you done graph theory with pictures?
 

1. What is graph theory without graphs?

Graph theory without graphs is a branch of mathematics that studies the properties and applications of graphs, but without actually using visual representations of graphs. Instead, it focuses on abstract concepts and mathematical models to analyze and solve problems.

2. Why study graph theory without graphs?

Graph theory without graphs is useful for solving complex problems in various fields such as computer science, social sciences, and engineering. It allows for a more efficient and systematic approach to problem-solving without relying on visual representations.

3. How is graph theory without graphs different from traditional graph theory?

The main difference between graph theory without graphs and traditional graph theory is the use of visual representations. Traditional graph theory relies heavily on visualizing graphs, while graph theory without graphs focuses more on abstract concepts and mathematical models.

4. What are some common applications of graph theory without graphs?

Graph theory without graphs has a wide range of applications, including network analysis, optimization problems, scheduling, and data analysis. It is also used in fields such as bioinformatics, transportation planning, and social network analysis.

5. Can graph theory without graphs be applied to real-world problems?

Yes, graph theory without graphs is highly applicable to real-world problems. It provides a powerful mathematical tool for analyzing complex systems and finding optimal solutions. Many real-world problems can be modeled and solved using concepts from graph theory without graphs.

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