explaination is awesome man i feel like why didnt i know about your channel before?..Im doing my post graduate so could you be able to put a clear explaination like this about 2 geodetic ,3 geodetic ,and upper geodetic graph ..please I really really neeed your favour sir..thank you for reading my comment and ill be waiting for your video
Absolutely! That is the complete graph denoted K1. Thanks for watching and for the question! And note that the reason why K1 is a complete graph is that it does technically satisfy the definition of complete graph. It is the case that every pair of distinct vertices in K1 is joined by an edge, it just so happens that there are no pairs of distinct vertices in K1, so it is "vacuously true".
what will be the size of graph of empty graph, null graph and trivial graph? In all these cases there is no edges, so according to the definition of size of graph or Cardinality of Edge set E will be zero. And what are the real life applications of these types of no edge graphs?
Thanks for watching and you are correct, the size of these graphs is 0. In real life if a situation had no edges, we wouldn't use graph theory to model it. I think the graphs are not useful, but they often behave a bit differently than other graphs, so these terms are useful when discussing and writing about graph theory. As in, "Let G be a nontrivial graph" before stating a property of all graphs that have more than one vertex. Or "the minimum degree of any non-empty graph is at least one". It is not true that the minimum degree of any graph is at least one, so the term "empty graph" helps us specify exactly which graphs have this property. Does that help?
Thanks for watching, did this video help clear it up at all? The terms are not universal in their usage, though thankfully these are all words for describing fairly unimportant objects anyways. The most important phrase related to these graphs I'd say is "nontrivial" which simply means a graph has more than one vertex (or more generally, it means a graph doesn't have only one vertex - so it could be a vertex with a self-loop if those are allowed).
3 months late but no from my understanding. G=(V,{}) where |V| = 1. G({1},{}) is saying the graph G has the vertex named 1, but the singular vertex in the trivial graph can have any name.
@@WrathofMath A graph whose vertex set is non-empty but edge set is empty is called a null graph. But in your definition, you have taught that a graph whose both, the vertex set and edge set are empty is a null graph.
A graph whose vertex set is non-empty but edge set is empty is SOMETIMES called a null graph, but in my experience it's more commonly called an empty graph. I find null graph is more commonly used to refer to the graph with no vertices and no edges, which is of course sometimes not considered a graph. This is precisely what I said in the lesson, that both definitions are used, so we must be careful when reading a text or paper that we know which is being used! I see you posted a link in another comment, but I cannot click it because TH-cam marks comments with links as spam, and doesn't allow me to review them (I can only see it in a preview that gives me an error when I try to look at it, it's tremendously irritating how TH-cam does this).
Thank You. This playlist is really helping me in my semester. Lots of love from India.
So glad to help, thanks for watching!
nice and simple videos. really helpful to understand as well as for a fast revision. its great.
Thank you, so glad you've found them helpful!
explaination is awesome man i feel like why didnt i know about your channel before?..Im doing my post graduate so could you be able to put a clear explaination like this about 2 geodetic ,3 geodetic ,and upper geodetic graph ..please I really really neeed your favour sir..thank you for reading my comment and ill be waiting for your video
How'd the rest of your postdoc go?
Great material, congrats!
Thank you for watching, I am glad you found it clear!
Thanks for making things clear.
2:24 is K1 = K1’ ?
I think that is fair to say.
Sir, Can a trivial graph on 1 vertex be also called a complete graph?
Absolutely! That is the complete graph denoted K1. Thanks for watching and for the question! And note that the reason why K1 is a complete graph is that it does technically satisfy the definition of complete graph. It is the case that every pair of distinct vertices in K1 is joined by an edge, it just so happens that there are no pairs of distinct vertices in K1, so it is "vacuously true".
Thank you sir 👍🏽
Is is fit for Applied Combinatorics written by Alan Tucker(By the way I think your video is great)
Can i write the empty graph like this K⁰?
what will be the size of graph of empty graph, null graph and trivial graph? In all these cases there is no edges, so according to the definition of size of graph or Cardinality of Edge set E will be zero.
And what are the real life applications of these types of no edge graphs?
Thanks for watching and you are correct, the size of these graphs is 0. In real life if a situation had no edges, we wouldn't use graph theory to model it. I think the graphs are not useful, but they often behave a bit differently than other graphs, so these terms are useful when discussing and writing about graph theory. As in, "Let G be a nontrivial graph" before stating a property of all graphs that have more than one vertex. Or "the minimum degree of any non-empty graph is at least one". It is not true that the minimum degree of any graph is at least one, so the term "empty graph" helps us specify exactly which graphs have this property. Does that help?
I was reading a book that refers to the empty book as the null graph.
and I got confused by this difference in meaning.
Thanks for watching, did this video help clear it up at all? The terms are not universal in their usage, though thankfully these are all words for describing fairly unimportant objects anyways. The most important phrase related to these graphs I'd say is "nontrivial" which simply means a graph has more than one vertex (or more generally, it means a graph doesn't have only one vertex - so it could be a vertex with a self-loop if those are allowed).
Can we define the trivial graph as
G=({1},{ } )?
And really thank you
3 months late but no from my understanding. G=(V,{}) where |V| = 1. G({1},{}) is saying the graph G has the vertex named 1, but the singular vertex in the trivial graph can have any name.
But it's k1' or a single node graph , that's never supposed to have any edges ?
That's what I think is trivial graph means
Thank you
This is coool❤
Nice video!
Thank you!
Give G=(V,E) what is the number number of edges of the Null graph with 6 vertices. whattt is thisss
Thanks
My pleasure, thanks for watching!
Something wrong with your Null Graph’s definition. Please check it.
I don't know what you mean, I provided the two common uses of the term. Was that part clear or did you have any questions I could help answer?
@@WrathofMath A graph whose vertex set is non-empty but edge set is empty is called a null graph. But in your definition, you have taught that a graph whose both, the vertex set and edge set are empty is a null graph.
A graph whose vertex set is non-empty but edge set is empty is SOMETIMES called a null graph, but in my experience it's more commonly called an empty graph. I find null graph is more commonly used to refer to the graph with no vertices and no edges, which is of course sometimes not considered a graph. This is precisely what I said in the lesson, that both definitions are used, so we must be careful when reading a text or paper that we know which is being used!
I see you posted a link in another comment, but I cannot click it because TH-cam marks comments with links as spam, and doesn't allow me to review them (I can only see it in a preview that gives me an error when I try to look at it, it's tremendously irritating how TH-cam does this).
null = K0?
🙏🙏🙏
Thanks for watching!
Anyone else feeling kinda empty after watching this lecture?