Which Sequences are Graphical? (Degree Sequences and Havel-Hakimi algorithm) | Graph Theory

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  • Опубліковано 9 лис 2024

КОМЕНТАРІ • 72

  • @WrathofMath
    @WrathofMath  2 місяці тому +1

    Support the production of this course by joining Wrath of Math as a Channel Member for exclusive and early videos, original music, and upcoming lecture notes for the graph theory series! Plus your comments will be highlighted for me so it is more likely I'll answer your questions!
    ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
    Graph Theory course: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
    Graph Theory exercises: ua-cam.com/play/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L.html

  • @Alex-fh4my
    @Alex-fh4my 6 місяців тому +5

    Thank you so much. My lecturer does not show any examples and just states theorems and proofs over and over again with no intuition behind these things. If only my tuition money could be going to people like you instead.

  • @minwoogwak99
    @minwoogwak99 Місяць тому +2

    Only 12 minutes of video saved my few hours for preparing exam

    • @WrathofMath
      @WrathofMath  Місяць тому

      Glad to help, thanks for watching!

  • @abie4830
    @abie4830 2 роки тому +2

    this channel should have atleast 500k subscribers

  • @teo_d_david
    @teo_d_david 3 роки тому +3

    took me like half an hour to understanbd it throught my uni book which didnt explain it at all and 5 minutes from your video. Keep it up! Thanks a lot!

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      So glad it helped! Thanks for watching and if you're looking for more graph theory, check out my playlist! ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

    • @teo_d_david
      @teo_d_david 3 роки тому

      @@WrathofMath Wow! Thanks. I have a sequence a=d1, d2... dn and one b=n-d1-1,..., n-dn-1, how can i prove this "prove a is graphical (iff) if only b is graphical". There are no numbers..

  • @nikhilmeena7258
    @nikhilmeena7258 Рік тому +3

    great setup, everything is decorated so well, that it is feeling soothing while watching the video

    • @WrathofMath
      @WrathofMath  Рік тому

      Thank you, that's exactly what I wanted to achieve with the Christmas videos! I wasn't able to do them last year simply because of time constraints, but if I can ever work on these full time, the Christmas set ups will be INTENSE.

  • @kartikeyasaraswat2736
    @kartikeyasaraswat2736 3 роки тому +5

    I'm a data science student and learning graph theory. I was having trouble understanding the concepts, thank god! that I found this channel. Sean, you're an amazing teacher, explanations are damn!.... I would really appreciate it if you could make some videos on the application of graph theory like stable allocation, pair matching, etc. Also, it'd be great to have some videos on topology and applications.

  • @tjllinas9102
    @tjllinas9102 3 роки тому +3

    these videos are more informative than the class im paying thousands of dollars to take lol. I appreciate them a lot man, keep it up!!

    • @WrathofMath
      @WrathofMath  3 роки тому +4

      I'm glad they've been helpful, thanks a lot for watching and let me know if you ever have any questions! Many more videos to come, and be sure to check out my Graph Theory playlist if you haven't already: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

    • @tcritt
      @tcritt 3 роки тому +1

      Same here, man. I was sent a load of pdfs at the start of the course and I'm expected to just read it all and assimilate it. Thank f**k for UA-cam and creators like this guy!

    • @PunmasterSTP
      @PunmasterSTP 5 місяців тому

      How'd the rest of your class go?

  • @ruscul7155
    @ruscul7155 2 роки тому +2

    this is the best video that ive been looking for.. thanks alot. just subbed

    • @WrathofMath
      @WrathofMath  2 роки тому

      Glad to help, thanks for your support!

  • @achuthas2875
    @achuthas2875 3 місяці тому

    So does “graphical” mean connected or disconnected graph? Also thank you for the precise explanation 🔥

  • @rikupt8092
    @rikupt8092 3 роки тому +4

    Great video, helped me a lot! I just have one question:
    If we have a multigraph then the 3 3 1 1 sequence would be possible since we could have the vertices with degree 3 connect to each other and each of them with 1 vertice of degree 1 and then just add a loop to the vertices of degree 3 making it possible?

    • @marylynnhayek3807
      @marylynnhayek3807 Рік тому

      So you want to connect the vertices of degree 3 with the vertices of degree 1, then connect the vertices of degree 3 with each other, and finally create a loop on the vertices of degree 3? i think the sequence would be : [5 5 1 1],

    • @marylynnhayek3807
      @marylynnhayek3807 Рік тому

      But if you only create a loop on the vertices of degree 3, all while connecting 1 vertex of degree 3 to a vertex of degree 1, i think it would then work. the sequence would stay the same. no need to connect the vertices of degree 3 with each other, since a loop is counted twice in a degree.

    • @mariap.9768
      @mariap.9768 Рік тому

      if loops and disconnected graphs are allowed, for a non directed graph:
      edges: (v1, v2),(v3, v4),(v3,v3),(v4,v4)
      d1 = d2 = 1,
      d3 = d4 = 2 + 1 = 3
      sequence 3,3,1,1
      However the algorithm used in the video is only for simple graphs.

    • @Wonderland_247
      @Wonderland_247 Рік тому

      Agreed! Surely in graph theory you could have one vertex with multiple loops coming off it. Then then number of edges will be greater then the number of vertices.

  • @tcritt
    @tcritt 3 роки тому

    @Wrath of Math - I came back for some last-minute revision. You should put "Havel-Hakimi" in the title. It will make it easier for people to find and you'll get the views it deserves.

    • @WrathofMath
      @WrathofMath  3 роки тому

      Thanks for the idea, you're right! I think I wasn't familiar with Havel-Hakimi name when I made this!

  • @aditichavan3427
    @aditichavan3427 2 роки тому +1

    Very Precise Information Given...Great 😃👍👍

  • @bytecode5834
    @bytecode5834 Рік тому

    Red is a bit distracting but the class is very good. Thanks for the video :)

  • @zhuoyangzhang4821
    @zhuoyangzhang4821 Рік тому +1

    OMG THIS IS WAY TOO HELPFUL TY VERY MUCHHH

  • @austinclark3439
    @austinclark3439 3 роки тому +1

    great video. In my discrete math class, I am told that using the Havel-Hakimi algorithm is helpful to determine if a degree sequence is graphical, like S5, but I am told that to constructively prove it's graphical, I still need to draw a graph with such a degree sequence.
    I am looking for helpful guide to drawing graphs from a degree sequence, knowing it is graphical. Advice? That'd be helpful. Start with the vertex of greatest degree, then draw them adjacent to the lesser degree vertices?

  • @PunmasterSTP
    @PunmasterSTP 5 місяців тому

    Havel-Hakimi? More like "Thanks for these lectures; yes indeed-y!" 🙏

  • @terriblegamer2050
    @terriblegamer2050 6 місяців тому

    Very helpful video. 🎉

    • @WrathofMath
      @WrathofMath  6 місяців тому

      Glad it was helpful! Thanks for watching!

  • @aditishelke6775
    @aditishelke6775 3 роки тому

    just in time for my test tomorrow.. thank you so much!!!
    Loving the christmas outfit :)

    • @WrathofMath
      @WrathofMath  3 роки тому +3

      You're very welcome! Good luck on the test and thank you - I'm enjoying the season, it'll be a bummer to go back to normal videos after the end of December, but I think people will be ready for it haha!

  • @joshyoo4041
    @joshyoo4041 3 роки тому

    Thank you for the video! is the theorem you used the Havel-Hakimi?

    • @WrathofMath
      @WrathofMath  3 роки тому

      My pleasure, thanks for watching! And I am not sure if the theorem is due to Havel and Hakimi, or if they just published algorithms using the theorem.

  • @samsunnahar9175
    @samsunnahar9175 2 місяці тому

    Thanks a lot for excellent video!!

    • @WrathofMath
      @WrathofMath  2 місяці тому

      Glad to help, thanks for watching!

  • @juanroa9304
    @juanroa9304 2 роки тому

    Thank you so much for this! you saved my life!!!

  • @gouravrout5769
    @gouravrout5769 2 роки тому

    thank u sir.....nice explanation ....INDIA

  • @flyinghigh3433
    @flyinghigh3433 7 місяців тому +1

    Thank you❤

  • @wishmanoor-fo7rp
    @wishmanoor-fo7rp Рік тому

    Thank you so much for such an informative video

  • @abenezeralemayehu5596
    @abenezeralemayehu5596 10 місяців тому

    i just love u u make my life easier

  • @ManuPela
    @ManuPela 11 місяців тому

    but does a lace not allow the sequence 3 3 1 1 to be done, with a lace on each of the 3s and by joining them you get to degree 3. And the other two 1 degress you just connect them to each other?

  • @sziluv
    @sziluv 3 роки тому +1

    thank you so much, you always help me.😊❤️

    • @WrathofMath
      @WrathofMath  3 роки тому

      You're very welcome, so glad I can help! Thanks for watching! 😀

  • @navpreetkaur5005
    @navpreetkaur5005 6 місяців тому

    While drawing the graph can't we draw the loops to show that it is graphical ....please explain as I have my exam coming

  • @Alex-ln5vb
    @Alex-ln5vb Рік тому

    Great great great! Thank you soooo much for the help

  • @haoruwen4105
    @haoruwen4105 2 роки тому

    Great video. thank you so much

  • @xxtuddlexx
    @xxtuddlexx 10 місяців тому

    oh baby the santa of math to save my fucking C in discrete 2 thank fuck your coloring video was clutch

    • @WrathofMath
      @WrathofMath  10 місяців тому

      Hell yeah - good luck my man!

  • @abhinandanbarua8677
    @abhinandanbarua8677 7 місяців тому

    The last sequence has odd number odd ones. How is it graphical?

  • @xxxxx409
    @xxxxx409 Рік тому

    thanks for the help!

  • @tcritt
    @tcritt 3 роки тому

    This was great. Thanks!

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      No problem, thanks for watching! If you're looking for more on graph theory, check out my playlist if you haven't yet: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

    • @tcritt
      @tcritt 3 роки тому

      @@WrathofMath Bookmarked!

  • @ItEngineer1998
    @ItEngineer1998 3 роки тому +6

    Capgemini brought me here 😂😂

    • @anupr7925
      @anupr7925 5 місяців тому

      And Cognizant brought me here 😂

    • @LearningCS-jp4cb
      @LearningCS-jp4cb 3 місяці тому

      @@anupr7925 Can i know for what reason? Are you guys preparing to appear for their aptitude exam or are these videos recommended for skill upgrade?

  • @7lool125
    @7lool125 3 місяці тому

    s3 could have 7 if there are loops? Am i wrong

  • @KihemboScovia
    @KihemboScovia 7 місяців тому

    Describe the conditions of the graph being graphical

  • @luciano8158
    @luciano8158 Рік тому

    awesome

  • @HghCVMrktingDelvrnce
    @HghCVMrktingDelvrnce Рік тому

    1:26

  • @devjyoti5614
    @devjyoti5614 Рік тому

    What about (3 2 1 0)

    • @WrathofMath
      @WrathofMath  Рік тому +1

      Not graphical, consider the fact that the first vertex needs to be adjacent to all the others, which is impossible because of the 0.

  • @navpreetkaur5005
    @navpreetkaur5005 6 місяців тому +1

    While drawing the graph can't we draw loops to show that it is graphical...please explain as I have my exam coming

    • @navpreetkaur5005
      @navpreetkaur5005 6 місяців тому

      Also pls tell that is {2,3,4,4,5} graphical is some multigraph possible to draw with this degree sequence