- 117
- 188 762
Ajeesh Ramanujan
India
เข้าร่วมเมื่อ 18 ก.ค. 2013
Video_117: A nonempty graph is bicolourable 2 chromatic if and only if is bipartite
In this video we prove the following characterisation of 2-chromatic graphs
A nonempty graph G is bicolourable (2-chromatic) if and only if G is bipartite.
A nonempty graph G is bicolourable (2-chromatic) if and only if G is bipartite.
มุมมอง: 1 629
วีดีโอ
Video_116: A graph is bicolourable 2 chromatic if and only if it has no odd cycles
มุมมอง 1.9K3 ปีที่แล้ว
In this video we prove the following characterisation of 2-chromatic graphs A graph is bicolourable (2-chromatic) if and only if it has no odd cycles.
Video_114: Vertex Colouring and Chromatic Number of a Graph
มุมมอง 6133 ปีที่แล้ว
In this video, we define Vertex Colouring and Chromatic Number of a Graph.
Video_115: Any Tree is 2 chromatic
มุมมอง 2.8K3 ปีที่แล้ว
In this video we prove the following statement Every tree with number of vertices greater than one vertices is 2-chromatic.
Video_113: Determining the distances between different pairs of vertices
มุมมอง 2623 ปีที่แล้ว
In this video we discuss a statement the helps us in finding the distance between two vertices in a graph by using the adjacency matrix of the graph.
Video_112: An observation about connectedness and adjacency matrix
มุมมอง 3143 ปีที่แล้ว
In this video we discuss a statement that helps us to determine whether a graph is connected or not using powers of the adjacency matrix of the graph.
Video_111 Powers of the Adjacency Matrix
มุมมอง 1.3K3 ปีที่แล้ว
In this video we prove a statement that helps to find the number of different edge sequences of length k between two vertices in a graph.
Video_110: Traces of the Adjacency Matrix of a Graph
มุมมอง 7363 ปีที่แล้ว
In this video we discuss the following statements related to the traces of the adjacency matrix of a graph. Let G be a simple undirected graph with m edges and t triangles. If X is the adjacency matrix of G, then (a) trace(X) = 0, (b) trace(X^2) = 2m, (c) trace(X^3) = 6t.
Video_109: Squares and Cubes of the Adjacency Matrix
มุมมอง 2.1K3 ปีที่แล้ว
In this video we discuss an interpretation of the square and cube of the adjacency matrix of a graph.
Video_108 Adjacency Matrix of a Graph
มุมมอง 4213 ปีที่แล้ว
In this video we define Adjacency Matrix of a Graph and look at some basic properties of it.
Video_107: Relation between incidence and path matrix of a graph
มุมมอง 4263 ปีที่แล้ว
In this video we prove the following relationship between the incidence matrix and path matrix of a graph If the columns of the incidence matrix A and the path matrix P(u, v) of a connected graph are arranged in the same order, then under the product (mod 2), AP^T (u, v) = M, where M is a matrix having ones in two rows u and v, and the zeros in the remaining n-2 rows.
Video_106: Path Matrix of a Graph
มุมมอง 9343 ปีที่แล้ว
In this video, we define the Path Matrix of a Graph.
Video_105: Relations among Reduced Incidence, Fundamental Cycle and Fundamental Cut set Matrices
มุมมอง 6393 ปีที่แล้ว
In this video, we prove a relationship among the Reduced Incidence Matrix, Fundamental Cycle Matrix and Fundamental Cut set Matrix of a Graph.
Video_104: Rank of the cut set Matrix of a Graph
มุมมอง 7733 ปีที่แล้ว
In this video we prove the following statement If G is a connected graph, then the rank of a cut-set matrix C(G) is equal to the rank of incidence matrix A(G), which equals the rank of graph G. Every circuit in a graph G has an even number of edges in common with any cut set: th-cam.com/video/yBuStjKH6oM/w-d-xo.html
Video_103: Cut Set Matrix and Fundamental Cut Set Matrix of a Graph
มุมมอง 3213 ปีที่แล้ว
In this video, we discuss the definition Cut Set Matrix and Fundamental Cut Set Matrix of a Graph.
Video_102: Rank of the Cycle Matrix of a Graph
มุมมอง 7933 ปีที่แล้ว
Video_102: Rank of the Cycle Matrix of a Graph
Video_101: Fundamental Cycle Matrix of a Graph.
มุมมอง 1.2K3 ปีที่แล้ว
Video_101: Fundamental Cycle Matrix of a Graph.
Video_100: Relationship between the Incidence Matrix and the Cycle Matrix of a Graph
มุมมอง 1.2K3 ปีที่แล้ว
Video_100: Relationship between the Incidence Matrix and the Cycle Matrix of a Graph
Video_99: Cycle (Circuit) Matrix of a Graph and its properties
มุมมอง 8283 ปีที่แล้ว
Video_99: Cycle (Circuit) Matrix of a Graph and its properties
Video_98: Sub-matrices of the Incidence Matrix and a property of it
มุมมอง 1.5K3 ปีที่แล้ว
Video_98: Sub-matrices of the Incidence Matrix and a property of it
Video_97: Reduced Incidence Matrix of a Graph
มุมมอง 8543 ปีที่แล้ว
Video_97: Reduced Incidence Matrix of a Graph
Video_94: A connected plane graph is bipartite if and only if its dual graph Eulerian.
มุมมอง 9693 ปีที่แล้ว
Video_94: A connected plane graph is bipartite if and only if its dual graph Eulerian.
Video_93: The edge e is a loop in G if and only if e* is a cut edge in the dual graph
มุมมอง 1533 ปีที่แล้ว
Video_93: The edge e is a loop in G if and only if e* is a cut edge in the dual graph
Video_92: The dual of a plane graph is planar
มุมมอง 1.2K3 ปีที่แล้ว
Video_92: The dual of a plane graph is planar
Video_89: Relationship between number of vertices and edges in homeomorphic graphs.
มุมมอง 2683 ปีที่แล้ว
Video_89: Relationship between number of vertices and edges in homeomorphic graphs.
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At 2:19, the {g,i} edge should be connected as well, otherwise the minimum degrees would not equal to 4.
Wonderfully explained Sir 🎉❤
Thank you sir.
Very well explained sir
Is fully needed to prove, because in the textbook they have mentioned a bit small only.
Background sound is disturbing,
Don't teach if you don't know
Great sir👍
Very good explanation sir
you should have taught how to convert non-planar to planar instead!
sir at 7:00 didint you draw 2 blue edges to the same point
Let G be a graph where δ(G) ≥ k. Prove that G has a path of length at least k. prove this as well please
AWESOME
Awesome 🤩
thanks really💚
What if the set s have edges with all the vertices in one component or both component then the proof wont work.
In full 3 Ary tree one internal was not having three children then how come it is full 3 ary?
please look at the definition
Awesome lecture
very nice
sir draw a tree of petersen graph
complement of G is wrong there should be edge b/w 4 to 3 also.
Thank u ❤
Exterior region is not a triangle
it should be called a 3 cycle
How to find minimum degree of the graph? Not getting. Please reply
The minimum number of edges incident on a vertex
Beautiful explaination sir...thak u
you skip things
Very wonderful lecture sir!! Thankyou
Thank you brother
Thank you sir
awesome video sir!!!
your explanation quality is very poor.try to improve it
Powerful message for me thank you
Use less 😏😏
Very confusing lecture
you did a very great job in trying to explain this question but It would be very nice of you to make it a little easy for younger audience as in 10th grade so that we can understand the topic
Best explanation I could find❤
Thankuuuu sir😇😇
Amazing, thanks for the video
Outstanding explanation sir🙏🙏
Not sure how you know that there is an eulerian trail between u,v in the last proof.
Because the graph G is connected.
Audio is not clear mannn....no use of this video
Thank you
thanks a lot!
Thanks Sir ❤️
Wonderful...
Thank you sir
Thank you sir 🙏
Thank you so much sir 🙏
Thank u so much sir 🙏