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In this problem, we have several directed graphs, and we're asked to find how many vertices and edges and determine the in and out degree of each of those.
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So let's take a look here.
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We are going to count our vertices.
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Our vertices are the dots.
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So we can count a, b, c, and d.
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So there are four vertices.
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And then we need to count our edges.
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Those are going to be these segments.
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So we have one, two, three, four, five, six, and seven.
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So we have seven edges.
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The second part of this problem wants us to find the in and out degree of each of these vertices.
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So i'm going to list out our vertices.
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We have vertex a, b, c, and d.
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I'm going to just make a like a little table.
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And out degree.
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So the n degree is how many arrows are pointing at a? so i have one, two, three pointing at a.
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Now for b we have one pointing at b.
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For c we have one, two, pointing at it.
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For c, we have one, two pointing at it.
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And for d, let me erase some of this so it's clear to see again.
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For d, we have zero coming into there.
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Now let's find.
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The out.
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How many ways can we leave a? we can only leave a one way.
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We can leave b, two ways.
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We can leave c one way.
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And we can leave d, one, two, three ways.
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So there's our in -out degrees for each of our vertices here.
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We'll repeat this process for this problem over here.
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Again, we have four a, b, c, and d, vertices.
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And we have one, two, three, four, five, six, seven, eight edges.
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Let's make our table again for our vertex, a, b, c, and d.
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Let's label it in and out.
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And let's just start counting how many ways we can get in to each one of these.
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So in to a would be one, two, two.
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Into b is going to be 1, 2, 3.
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Into c is going to be 1, 2.
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And then into d is just the 1.
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He's over here by himself.
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And then we'll count our outs.
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Let's count out of a.
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We can leave a just one way right here.
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We can leave b this way, two, three, or four, we can leave c just the one way, and we can only leave d one way as well...