Disjoint union of graphs
Okay kiddo, let me explain what a disjoint union of graphs means. Imagine you have two sets of toys, one set has a few toy cars and the other set has some toy animals. Now, if you put all the cars and animals together, you will have a big set of toys with both cars and animals mixed up, right? But what if you want to keep the two sets separate and not mix them up? Then you would want to have two different sets of toys, one with only cars and the other with only animals, right?
Well, this is similar to a disjoint union of graphs. Instead of toys, we have graphs which are made up of points or vertices connected by lines or edges. When we talk about a disjoint union of two graphs, we mean that we want to keep the two graphs separated and not mix them up. So, just like the two sets of toys, we will have two different graphs, each with their own vertices and edges.
Let's say we have two graphs, one with three vertices and two edges and the other with two vertices and one edge. We can create a disjoint union of these two graphs by putting them side by side but not mixing them up. So we will have a graph with five vertices in total (3+2) and three edges in total (2+1). However, there will be no edges connecting the vertices in one graph to the vertices in the other graph, just like there aren't any toy cars in the set of toys with animals.
So, to sum it up, a disjoint union of graphs means that we keep two graphs separate and don't mix them up, just like we keep two sets of toys separate and don't mix them up.
Well, this is similar to a disjoint union of graphs. Instead of toys, we have graphs which are made up of points or vertices connected by lines or edges. When we talk about a disjoint union of two graphs, we mean that we want to keep the two graphs separated and not mix them up. So, just like the two sets of toys, we will have two different graphs, each with their own vertices and edges.
Let's say we have two graphs, one with three vertices and two edges and the other with two vertices and one edge. We can create a disjoint union of these two graphs by putting them side by side but not mixing them up. So we will have a graph with five vertices in total (3+2) and three edges in total (2+1). However, there will be no edges connecting the vertices in one graph to the vertices in the other graph, just like there aren't any toy cars in the set of toys with animals.
So, to sum it up, a disjoint union of graphs means that we keep two graphs separate and don't mix them up, just like we keep two sets of toys separate and don't mix them up.