dan815
  • dan815
magic labelling, a edge numbering with number 1,2,3...,q for a q edge graph is said to be magic if the numbers around a vertex all add upto the same number Find a magic labelling for k(3,3), using the numbers 1,2,3,...,9
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
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dan815
  • dan815
ill show a solution to this one, apparently theres some neat stuff it translates to
dan815
  • dan815
|dw:1447321583566:dw|
dan815
  • dan815
|dw:1447321622111:dw|

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dan815
  • dan815
see how every edge has 2 adj vertices and the column numbers from the magic square go on one vertex and the row numbesr go on other,
dan815
  • dan815
and u can repeat this process to get a magic labelling
dan815
  • dan815
so how does this really translate, how many solutions are there, what does a 4 by 4 magic squars picture look like
dan815
  • dan815
|dw:1447321789878:dw|
lochana
  • lochana
you can't use the same number twice. right?
dan815
  • dan815
yes
lochana
  • lochana
I am confused now, well it depends on 'q' and the number that sum up to. for example you can't do this for 4 by 4 magic square since we only have 9 numbers
dan815
  • dan815
can u try this problem
lochana
  • lochana
wait. if it's 4 by 4, q = 16 5 by 5, q = 25 6 by 6 , q= 36 and so on..
dan815
  • dan815
What sit he sum at each vertex in a magic labelling of k_n,n
dan815
  • dan815
like for any n by n magic square can u determine what the row and colums must add upto
dan815
  • dan815
the number keeps coming out to the average number * n
dan815
  • dan815
for 3 by 3 ther are 9 numbers, 5 is the middle number 5*3 =15 is the sum of rows and colums of the magic square
dan815
  • dan815
same thing for 4 by 4 numbers 1 to 16, 8.5 is avg 8.5*5=34 , 34 is the sum of rows and columns
dan815
  • dan815
why must this be the only possible way
dan815
  • dan815
http://prntscr.com/91vj1g
dan815
  • dan815
that should say 8.5*4=34
dan815
  • dan815
why is it happening, how to get the more general case?
lochana
  • lochana
do you have questions before these two?
dan815
  • dan815
no
dan815
  • dan815
those are first 2 questions in this section
lochana
  • lochana
well. let's tag people here.
lochana
  • lochana
@ganeshie8 @Directrix
dan815
  • dan815
1 Attachment
dan815
  • dan815
i took screenshots of the whole section notes
dan815
  • dan815
the first 3 pages should cover what we need the rest is other stuff
lochana
  • lochana
nice. I will go through it.

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