Tensor product of graphs
Imagine you have a bunch of toys. Each toy is made up of different parts. For example, a car has wheels, a body, and other things. Now, let's say you have two different toys: a car and a bike.
When we talk about the tensor product of graphs, think of each graph as a toy. Just like the car and the bike are made up of different parts, a graph is made up of different points and lines connecting them.
When we take the tensor product of two graphs, it's like combining the car and the bike together to create a new toy. But instead of combining the parts of the toys, we combine the points and lines of the graphs.
To do this, we take each point from the first graph and connect it to every point in the second graph. So if the first graph has 3 points and the second graph has 4 points, we will have 3x4 = 12 new points in the combined graph.
Next, we connect each of these newly created points in the combined graph according to the connections in the original graphs. For example, if point A in the first graph was connected to point B, and point X in the second graph was connected to point Y, then in the combined graph, the new point A' (created from point A in the first graph) will be connected to the new point X' (created from point X in the second graph).
This process is repeated for every pair of points in the original graphs, resulting in a combined graph that has all the points and connections from both graphs.
So, just like combining the car and the bike together creates a new toy with all the parts from both toys, combining two graphs using the tensor product creates a new graph with all the points and connections from both graphs.
When we talk about the tensor product of graphs, think of each graph as a toy. Just like the car and the bike are made up of different parts, a graph is made up of different points and lines connecting them.
When we take the tensor product of two graphs, it's like combining the car and the bike together to create a new toy. But instead of combining the parts of the toys, we combine the points and lines of the graphs.
To do this, we take each point from the first graph and connect it to every point in the second graph. So if the first graph has 3 points and the second graph has 4 points, we will have 3x4 = 12 new points in the combined graph.
Next, we connect each of these newly created points in the combined graph according to the connections in the original graphs. For example, if point A in the first graph was connected to point B, and point X in the second graph was connected to point Y, then in the combined graph, the new point A' (created from point A in the first graph) will be connected to the new point X' (created from point X in the second graph).
This process is repeated for every pair of points in the original graphs, resulting in a combined graph that has all the points and connections from both graphs.
So, just like combining the car and the bike together creates a new toy with all the parts from both toys, combining two graphs using the tensor product creates a new graph with all the points and connections from both graphs.