<p>Any value or interest in a formula that calculates (not look up) the 'integer order' of a given 'Independent Edge Set' OR given an 'Independent Set' calculates the 'integer order' on Complete Graphs? The Mappings of Perfect Matchings on a Complete Graph. Likewise for Cliques.</p>
<p>Example:
n=8, k=2
vertices: 8
edge count: 28
perfect matchings: 105
vertice set: {1,2,3,4,5,6,7,8}</p>
<p>Order: Independent Edge Set (Perfect Matching)
1: {1,2}{3,4}{5,6}{7,8}
2: {1,2}{3,4}{5,7}{6,8}
3: {1,2}{3,4}{5,8}{6,7}
…
105: {1,8}{2,7}{3,6}{4,5}</p>

CC BY-SA 4.0
2023-11-16T03:31:57.707Z
Applies to any integer 'k' as well. ie: n=9,k=3. ({1,2,3}{4,5,6}{7,8,9}...
Tim
CC BY-SA 4.0
2023-11-16T03:37:23.990Z
I ask because I can do this and have a proof that it is always accurate. And, I am not aware of the existence of anything similar.
Tim
<cc.complexity-theory><graph-theory><np-complete><clique><independent-set>
Any value in a formula that calculates (not look up) the 'order' of a 'Independent Edge Set' OR a 'I.E.S.' given an 'order' on complete graphs?
Tim
# Any value in a formula that calculates (not look up) the 'order' of a 'Independent Edge Set' OR a 'I.E.S.' given an 'order' on complete graphs?

(Asked by: username_0 on 2023-11-16)

Any value or interest in a formula that calculates (not look up) the 'integer order' of a given 'Independent Edge Set' OR given an 'Independent Set' calculates the 'integer order' on Complete Graphs? The Mappings of Perfect Matchings on a Complete Graph. Likewise for Cliques.

Example:
n=8, k=2
vertices: 8
edge count: 28
perfect matchings: 105
vertice set: {1,2,3,4,5,6,7,8}

Order: Independent Edge Set (Perfect Matching)
1: {1,2}{3,4}{5,6}{7,8}
2: {1,2}{3,4}{5,7}{6,8}
3: {1,2}{3,4}{5,8}{6,7}
…
105: {1,8}{2,7}{3,6}{4,5}

**Tags:** cc.complexity-theory, graph-theory, np-complete, clique, independent-set
> **Comments:**
> **username_0**: Applies to any integer 'k' as well. ie: n=9,k=3. ({1,2,3}{4,5,6}{7,8,9}...  
> **username_0**: I ask because I can do this and have a proof that it is always accurate. And, I am not aware of the existence of anything similar.  

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## 0 answers

