Subtracting a Vertex from a Graph (Vertex Deletion) | Graph Theory
How do we subtract a vertex from a graph? This is also sometimes referred to as deleting a vertex from a graph. So call it vertex subtraction or vertex deletion, whichever you please, that’s what we are going over today!
Deleting a vertex from a graph is pretty intuitive. First we just remove the vertex from the graph, but then we also have to remove any edges that were incident to that vertex! We cannot have an edge that has an endpoint that isn’t in the graph, so once the vertex goes, its incident edges have to go to! What you’ll find if you try this on complete graphs is that deleting a vertex from a complete graph K_{n} just gives you the complete graph K_{n-1}! That’s pretty neat, and easy to prove if you’re interested!
We also discuss cut vertices briefly in this lesson. If deleting a vertex v from a graph G results in a graph with more components, that is: if G - v has more components than G, then we call v a “cut vertex” because it “cuts“ the graph so to speak!
If you're taking a course in Graph Theory, or preparing to, you may be interested in the textbook that introduced me to Graph Theory: “A First Course in Graph Theory“ by Gary Chartrand and Ping Zhang. It’s a wonderful text! You can purchase this book through my Amazon affiliate link below! Using the affiliate link costs you nothing extra, and helps me continue to work on Wrath of Math!
PURCHASE "A First Course in Graph Theory": https://amzn.to/31hgvvJ
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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