GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
95 views
Decomposition of complete graph into cycles through all vertices.
Continuing explanation [here][1],
Next explanation is given as

for $n=5$ , $n=7$, it suffices to use cycles formed by traversing the
vertices with constant difference:$\left(0,1,2,3,4\right)$,$\left(0,2,4,1,3\right)$ for $n=5 $

and

$\left(0,1,2,3,4,5,6\right)$,$\left(0,3,6,2,5,1,4\right)$ for $n=7 $

Not getting how
$\left(0,1,2,3,4\right)$,$\left(0,2,4,1,3\right)$  and  $\left(0,1,2,3,4,5,6\right)$,$\left(0,3,6,2,5,1,4\right)$ is coming from !!!!!

Please help me out!!

  [1]: http://math.stackexchange.com/questions/1985647/decomposition-of-complete-graph-into-cycles-through-all-vertices/1985652#1985652
asked in Graph Theory by (143 points)   | 95 views
The link that you have provided gives number of cycles in graph. But, in the example that you have given has some pattern.
but it is coming cycle rt?

Draw a complete graph with 5 vertices . (0,1,2,3,4) ,(0,2,4,1,3) both forming cycles
Yes, but answer would be different

Please log in or register to answer this question.



Top Users May 2017
  1. akash.dinkar12

    3152 Points

  2. pawan kumarln

    1630 Points

  3. sh!va

    1590 Points

  4. Arjun

    1350 Points

  5. Devshree Dubey

    1246 Points

  6. Angkit

    1044 Points

  7. Debashish Deka

    1022 Points

  8. Bikram

    972 Points

  9. LeenSharma

    820 Points

  10. Prashant.

    692 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 22 - 28
  1. pawan kumarln

    256 Points

  2. Ahwan

    232 Points

  3. jjayantamahata

    114 Points

  4. joshi_nitish

    114 Points

  5. Arnab Bhadra

    94 Points


22,731 questions
29,061 answers
65,094 comments
27,625 users