Ajeesh Ramanujan
Ajeesh Ramanujan
  • Видео 117
  • Просмотров 198 514

Видео

Video_116: A graph is bicolourable 2 chromatic if and only if it has no odd cycles
Просмотров 2 тыс.3 года назад
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
Просмотров 6343 года назад
In this video, we define Vertex Colouring and Chromatic Number of a Graph.
Video_115: Any Tree is 2 chromatic
Просмотров 3 тыс.3 года назад
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
Просмотров 2704 года назад
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
Просмотров 3254 года назад
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
Просмотров 1,3 тыс.4 года назад
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
Просмотров 7694 года назад
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
Просмотров 2,2 тыс.4 года назад
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
Просмотров 4304 года назад
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
Просмотров 4434 года назад
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
Просмотров 1 тыс.4 года назад
In this video, we define the Path Matrix of a Graph.
Video_105: Relations among Reduced Incidence, Fundamental Cycle and Fundamental Cut set Matrices
Просмотров 6764 года назад
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
Просмотров 8054 года назад
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: ruclips.net/video/yBuStjKH6oM/видео.html
Video_103: Cut Set Matrix and Fundamental Cut Set Matrix of a Graph
Просмотров 3324 года назад
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
Просмотров 8264 года назад
Video_102: Rank of the Cycle Matrix of a Graph
Video_101: Fundamental Cycle Matrix of a Graph.
Просмотров 1,4 тыс.4 года назад
Video_101: Fundamental Cycle Matrix of a Graph.
Video_100: Relationship between the Incidence Matrix and the Cycle Matrix of a Graph
Просмотров 1,2 тыс.4 года назад
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
Просмотров 8714 года назад
Video_99: Cycle (Circuit) Matrix of a Graph and its properties
Video_98: Sub-matrices of the Incidence Matrix and a property of it
Просмотров 1,5 тыс.4 года назад
Video_98: Sub-matrices of the Incidence Matrix and a property of it
Video_97: Reduced Incidence Matrix of a Graph
Просмотров 8744 года назад
Video_97: Reduced Incidence Matrix of a Graph
Video_96: Rank of the incidence matrix
Просмотров 7 тыс.4 года назад
Video_96: Rank of the incidence matrix
Video_95: Incidence Matrix of a Graph
Просмотров 3704 года назад
Video_95: Incidence Matrix of a Graph
Video_94: A connected plane graph is bipartite if and only if its dual graph Eulerian.
Просмотров 1 тыс.4 года назад
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
Просмотров 1614 года назад
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
Просмотров 1,2 тыс.4 года назад
Video_92: The dual of a plane graph is planar
Video_91: Self dual Graphs
Просмотров 1,5 тыс.4 года назад
Video_91: Self dual Graphs
Video_90: Dual of a Plane Graph
Просмотров 3884 года назад
Video_90: Dual of a Plane Graph
Video_89: Relationship between number of vertices and edges in homeomorphic graphs.
Просмотров 3004 года назад
Video_89: Relationship between number of vertices and edges in homeomorphic graphs.
Video_88: Petersen Graph is Non planar
Просмотров 7 тыс.4 года назад
Video_88: Petersen Graph is Non planar

Комментарии

  • @sreelakshmimr8706
    @sreelakshmimr8706 5 дней назад

    Sir,is this necessary to make fundamental cut matrix in to two parts when we write matrix?after this partition only we can say this matrix fundamental cut matrix?when we divide like this it's submatrix propery doesn't exist??

  • @MukeshKumar369-c6e
    @MukeshKumar369-c6e Месяц назад

    but sir which vertex is peripheral vertex the v1 have accentricity is diameter as you see distance between v2 is also diamter so which one is diameter is little bit confusion?

  • @MukeshKumar369-c6e
    @MukeshKumar369-c6e Месяц назад

    there is noise in your lecture🤏

  • @MukeshKumar369-c6e
    @MukeshKumar369-c6e Месяц назад

    nice sir but there is extra noise in your lecture why is this.

  • @vickymronga8998
    @vickymronga8998 Месяц назад

    Very good video, thank you so much

  • @sadabali1228
    @sadabali1228 2 месяца назад

    ❤❤❤

  • @陸月飴
    @陸月飴 2 месяца назад

    At 2:19, the {g,i} edge should be connected as well, otherwise the minimum degrees would not equal to 4.

  • @Sauravbhaduka2
    @Sauravbhaduka2 3 месяца назад

    Wonderfully explained Sir 🎉❤

  • @avanishverma6049
    @avanishverma6049 3 месяца назад

    Thank you sir.

  • @dhanyanayak5240
    @dhanyanayak5240 4 месяца назад

    Very well explained sir

  • @Deepak-ly3pl
    @Deepak-ly3pl 4 месяца назад

    Is fully needed to prove, because in the textbook they have mentioned a bit small only.

  • @jyotihiremath1338
    @jyotihiremath1338 4 месяца назад

    Background sound is disturbing,

  • @PojithaReddy-lb2ck
    @PojithaReddy-lb2ck 5 месяцев назад

    Don't teach if you don't know

  • @Rose2369p
    @Rose2369p 5 месяцев назад

    Great sir👍

  • @Rose2369p
    @Rose2369p 5 месяцев назад

    Very good explanation sir

  • @keerthanadhami
    @keerthanadhami 6 месяцев назад

    you should have taught how to convert non-planar to planar instead!

  • @geckovlr
    @geckovlr 6 месяцев назад

    sir at 7:00 didint you draw 2 blue edges to the same point

  • @ahsanulhaq8056
    @ahsanulhaq8056 8 месяцев назад

    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

  • @AadhavSankar
    @AadhavSankar 8 месяцев назад

    AWESOME

  • @antonyjosekavalakatt1905
    @antonyjosekavalakatt1905 8 месяцев назад

    Awesome 🤩

  • @lazyginger5310
    @lazyginger5310 9 месяцев назад

    thanks really💚

  • @adithyabharath6453
    @adithyabharath6453 10 месяцев назад

    What if the set s have edges with all the vertices in one component or both component then the proof wont work.

  • @Pooja-n5v8h
    @Pooja-n5v8h 10 месяцев назад

    In full 3 Ary tree one internal was not having three children then how come it is full 3 ary?

  • @AMARSINGH-uk9js
    @AMARSINGH-uk9js 10 месяцев назад

    Awesome lecture

  • @mageshnanjundan930
    @mageshnanjundan930 Год назад

    very nice

  • @mansornasrat-lx3oq
    @mansornasrat-lx3oq Год назад

    sir draw a tree of petersen graph

  • @sudhanshusagar5762
    @sudhanshusagar5762 Год назад

    complement of G is wrong there should be edge b/w 4 to 3 also.

  • @Easystudy08
    @Easystudy08 Год назад

    Thank u ❤

  • @rsg4666
    @rsg4666 Год назад

    Exterior region is not a triangle

    • @geckovlr
      @geckovlr 6 месяцев назад

      it should be called a 3 cycle

  • @ayeshahafiz2002
    @ayeshahafiz2002 Год назад

    How to find minimum degree of the graph? Not getting. Please reply

    • @majidibnsayeeda
      @majidibnsayeeda 5 месяцев назад

      The minimum number of edges incident on a vertex

  • @sharathkumar.h.t.sharathku9652

    Beautiful explaination sir...thak u

  • @umaidmanzoor5659
    @umaidmanzoor5659 Год назад

    you skip things

  • @Rose2369p
    @Rose2369p Год назад

    Very wonderful lecture sir!! Thankyou

  • @aqibrehman8693
    @aqibrehman8693 Год назад

    Thank you brother

  • @sharathkumar.h.t.sharathku9652

    Thank you sir

  • @kundanpratapmusic675
    @kundanpratapmusic675 Год назад

    awesome video sir!!!

  • @Mdsajidahsanseyamstudent
    @Mdsajidahsanseyamstudent Год назад

    your explanation quality is very poor.try to improve it

  • @PreeteKanwal
    @PreeteKanwal Год назад

    Powerful message for me thank you

  • @Bheemfoundation-12
    @Bheemfoundation-12 Год назад

    Use less 😏😏

  • @anuragbandyopadhyay3483
    @anuragbandyopadhyay3483 Год назад

    Very confusing lecture

  • @INMO2776
    @INMO2776 Год назад

    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

  • @user-jc5vo9sz3l
    @user-jc5vo9sz3l Год назад

    Best explanation I could find❤

  • @MAMTARANI-gi2ox
    @MAMTARANI-gi2ox Год назад

    Thankuuuu sir😇😇

  • @vickymronga8998
    @vickymronga8998 Год назад

    Amazing, thanks for the video

  • @anandpaul2707
    @anandpaul2707 Год назад

    Outstanding explanation sir🙏🙏

  • @benjaminandersson2572
    @benjaminandersson2572 2 года назад

    Not sure how you know that there is an eulerian trail between u,v in the last proof.

    • @PubicGore
      @PubicGore 10 месяцев назад

      Because the graph G is connected.

  • @shwetasingh3670
    @shwetasingh3670 2 года назад

    Audio is not clear mannn....no use of this video

  • @chandrachandra3356
    @chandrachandra3356 2 года назад

    Thank you

  • @thefatheram
    @thefatheram 2 года назад

    thanks a lot!

  • @RaviKumar-ik3jn
    @RaviKumar-ik3jn 2 года назад

    Thanks Sir ❤️