Parity graph
Ok kiddo, so imagine you have a bunch of toys that you want to put into two different boxes. You want to make sure that each box has the same number of toys when you're finished.
A parity graph is kind of like that. It's a way to look at a bunch of points (or nodes) and figure out if they can be divided into two groups (or sets) with the same number of points in each set.
But instead of toys, we're talking about numbers. Each point in the graph represents a different number. And we use lines (or edges) to connect points that are related to one another in some way.
Now, to figure out if the points can be divided into two sets with the same number of points in each set, we use a special rule called the parity rule.
The parity rule says that each time we go along a line (or edge) in the graph, we have to change our count. So if we start at a point and go along one line, we count it as 1. But if we go along another line, we have to switch to counting as 0. And then if we go along another line, we switch back to counting as 1 again.
We keep switching back and forth like this as we move along the lines in the graph. And when we get to the end of the lines, we add up all the values we counted. If the total is an even number, then we know we can divide the points into two sets with the same number of points in each set. But if the total is an odd number, then we can't divide them evenly into two sets.
So, in summary, a parity graph is a way to look at a bunch of numbers and connections between them. We use a special rule called the parity rule to figure out if we can divide the numbers into two sets with the same number of numbers in each set.
A parity graph is kind of like that. It's a way to look at a bunch of points (or nodes) and figure out if they can be divided into two groups (or sets) with the same number of points in each set.
But instead of toys, we're talking about numbers. Each point in the graph represents a different number. And we use lines (or edges) to connect points that are related to one another in some way.
Now, to figure out if the points can be divided into two sets with the same number of points in each set, we use a special rule called the parity rule.
The parity rule says that each time we go along a line (or edge) in the graph, we have to change our count. So if we start at a point and go along one line, we count it as 1. But if we go along another line, we have to switch to counting as 0. And then if we go along another line, we switch back to counting as 1 again.
We keep switching back and forth like this as we move along the lines in the graph. And when we get to the end of the lines, we add up all the values we counted. If the total is an even number, then we know we can divide the points into two sets with the same number of points in each set. But if the total is an odd number, then we can't divide them evenly into two sets.
So, in summary, a parity graph is a way to look at a bunch of numbers and connections between them. We use a special rule called the parity rule to figure out if we can divide the numbers into two sets with the same number of numbers in each set.