Subtracting a Vertex from a Graph (Vertex Deletion) | Graph Theory
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- เผยแพร่เมื่อ 14 ก.ย. 2019
- 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": 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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Vertex deletion? More like "Very cool videos you're makin'!" 👍
thanks for your generosity in science
It is my pleasure, thank you for watching!
Thanks now clearly understood
You're very welcome, I am glad it was clear!
Fantastic
clearly defined
I'm glad it was clear, thanks a lot for watching!
يعطيك العافيه شكرا لك .
Is vertex subtraction is called induced sub graph ?
Explain complementary graphs kindly.
We can remove any of the vertices??
Thanks for watching, and yes we absolutely can. We can remove any vertex, and we can also remove any n vertices from a graph that has at least n vertices. Of course, it is interesting to study the properties a graph might have after deleting vertices. We consider these sorts of things when discussing vertex connectivity, for example.
@@WrathofMath thanks for your reply
Can u make a video on exponential distribution.
Love from India
Hi Abhishek, thanks for watching and for your request! That’s a great topic to cover. You may know I love probability theory, so I’ll try to get to it soon!
Here it is, thanks again for the request! th-cam.com/video/GXD9r8j3XKc/w-d-xo.html
This one was a lot of fun to do, I hope it helps! I think it’s the first time I’ve done integration on this channel, so it’s an exciting lesson!
thxxxxxxxxxxxxxxxxxxxx
My pleasure! Thanks for watching and if you're looking for more graph theory, check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html