Graph of groups

A graph of groups is like a big map that shows different groups, but instead of cities and countries, we have shapes that represent groups of things. Each shape is called a vertex.

Let's say we have three different groups represented by three different shapes: a circle, a square, and a triangle. These three shapes are connected by lines, called edges.

Now, imagine that each shape (circle, square, triangle) represents a group of friends, and each edge between the shapes represents a relationship between those groups. For example, the circle group might be friends with the triangle group, and the square group might be friends with both the circle and triangle groups.

But, here's where things get more complicated. Each group might have a rule or law that they follow within the group. For example, the circle group might have a rule that says "everyone must wear blue shirts" and the triangle group might have a rule that says "everyone must wear green shirts."

So, when these groups interact with each other (represented by the edges in the graph of groups), they might have to come up with a new rule that combines their existing rules.

For example, when the circle and triangle groups come together, they might say "let's all wear blue-green shirts!" And when the square group joins in, they might have to figure out a way to combine all three rules. This process of combining rules and figuring out how different groups can work together is called "group theory."

Overall, a graph of groups is a way of showing how different groups relate to each other and how they can collaborate and work together, even if they have different rules or ways of doing things.