meditationatae

Just another WordPress.com site

Data on possible/probable 15-vertex, 37-edge unit distance graph

Note: copied from the output of a computer program.

===

adjacency matrix:
0 0 0 0 0 1 1 1 0 0 0 0 1 0 0
0 0 1 0 1 1 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 1 0 0 1 0 0 0 1
0 0 0 0 0 1 0 1 0 1 1 1 0 0 0
0 1 0 0 0 0 1 1 0 1 0 0 0 1 0
1 1 0 1 0 0 0 0 0 0 0 1 1 0 0
1 0 0 0 1 0 0 1 1 0 0 1 0 0 1
1 0 1 1 1 0 1 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0 1 1 1 1 0
0 0 0 1 1 0 0 0 0 0 0 1 0 1 0
0 0 1 1 0 0 0 1 1 0 0 0 1 1 0
0 0 0 1 0 1 1 0 1 1 0 0 0 0 0
1 0 0 0 0 1 0 0 1 0 1 0 0 0 0
0 1 0 0 1 0 0 0 1 1 1 0 0 0 0
0 0 1 0 0 0 1 0 0 0 0 0 0 0 0

post adjacency matrix:
0 0 0 0 0 1 1 1 0 0 0 0 1 0 0
0 0 1 0 1 1 0 0 0 0 0 0 0 1 1
0 1 0 0 0 0 0 1 0 0 1 0 0 0 1
0 0 0 0 0 1 0 1 0 1 1 1 0 0 0
0 1 0 0 0 0 1 1 0 1 0 0 0 1 0
1 1 0 1 0 0 0 0 0 0 0 1 1 0 0
1 0 0 0 1 0 0 1 1 0 0 1 0 0 1
1 0 1 1 1 0 1 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0 1 1 1 1 1
0 0 0 1 1 0 0 0 0 0 0 1 0 1 0
0 0 1 1 0 0 0 1 1 0 0 0 1 1 0
0 0 0 1 0 1 1 0 1 1 0 0 0 0 0
1 0 0 0 0 1 0 0 1 0 1 0 0 0 0
0 1 0 0 1 0 0 0 1 1 1 0 0 0 0
0 1 1 0 0 0 1 0 1 0 0 0 0 0 0

total_finds = 43
Tests count = 15 has_converged_step = 2616 max_has_converged_step = 2616
rec_diff1 = 39.857967
rec_diff25 = 5.935028
rec_diff50 = 2.601235
rec_diff100 = 0.381244
rec_diff200 = 0.069902
rec_diff400 = 0.005289
rec_diff800 = 0.0000311393226121
rec_diff1200 = 0.0000001835105382
probable_unit_lengths = 37
graph is 3-colorable:no.
count_4_colorings = 364 num_4_colorings_mod_24 = 0
Matrix of distances vertex to vertex:
A B C D E F G H I J K L M N O
A 0.00 1.57 0.58 1.95 1.73 1.00 1.00 1.00 1.95 2.73 1.46 1.91 1.00 2.43 1.46
B 1.57 0.00 1.00 1.57 1.00 1.00 0.58 1.46 0.46 1.73 0.58 0.74 0.74 1.00 1.00
C 0.58 1.00 0.00 1.73 1.37 0.74 0.46 1.00 1.37 2.35 1.00 1.44 0.46 1.91 1.00
D 1.95 1.57 1.73 0.00 0.58 1.00 1.46 1.00 1.95 1.00 1.00 1.00 1.91 1.46 2.43
E 1.73 1.00 1.37 0.58 0.00 0.74 1.00 1.00 1.37 1.00 0.46 0.46 1.44 1.00 1.91
F 1.00 1.00 0.74 1.00 0.74 0.00 0.58 0.46 1.46 1.73 0.58 1.00 1.00 1.57 1.57
G 1.00 0.58 0.46 1.46 1.00 0.58 0.00 1.00 1.00 1.95 0.58 1.00 0.46 1.46 1.00
H 1.00 1.46 1.00 1.00 1.00 0.46 1.00 0.00 1.91 1.91 1.00 1.37 1.37 1.95 1.95
I 1.95 0.46 1.37 1.95 1.37 1.46 1.00 1.91 0.00 1.91 1.00 1.00 1.00 1.00 1.00
J 2.73 1.73 2.35 1.00 1.00 1.73 1.95 1.91 1.91 0.00 1.37 1.00 2.35 1.00 2.73
K 1.46 0.58 1.00 1.00 0.46 0.58 0.58 1.00 1.00 1.37 0.00 0.46 1.00 1.00 1.46
L 1.91 0.74 1.44 1.00 0.46 1.00 1.00 1.37 1.00 1.00 0.46 0.00 1.37 0.58 1.73
M 1.00 0.74 0.46 1.91 1.44 1.00 0.46 1.37 1.00 2.35 1.00 1.37 0.00 1.73 0.58
N 2.43 1.00 1.91 1.46 1.00 1.57 1.46 1.95 1.00 1.00 1.00 0.58 1.73 0.00 1.95
O 1.46 1.00 1.00 2.43 1.91 1.57 1.00 1.95 1.00 2.73 1.46 1.73 0.58 1.95 0.00

TBC …

===

Added:  Mon Mar 20 04:02:36 EDT 2017

A reminder:

Thomas Sauvaget who has a blog named

episodic thoughts

found a 16-vertex graph consisting approximately of two

Moser spindles, plus two more points in a special

configuration:

https://thomas1111.wordpress.com/2015/01/03/on-a-certain-4-chromatic-planar-graph/

He writes in part:

As it happens, if we enforce unit distances at 6~14 and 10~14 then the abscissa of vertex #14 is not 0.5 (which would make things work), but instead

-\frac{895702085}{177666094271969928} \sqrt{514527538436665}+ \frac{415413875483399597}{676176985277553384} \approx 0.49999956608   (and same problem with vertex #15).  ”

===

 

So, I’m thinking that I should not be assuming that vertices in an embedded graph are a unit apart, just because they are 1.0 units apart to within 0.0000001  …

Perhaps I can use the MPFR library, or PARI/gp to

calculate distances between points that appear to be 1.0 units apart, to 50 or more decimals or significant figures …

 

 

Advertisements

Written by meditationatae

March 20, 2017 at 8:00 am

Posted in History

%d bloggers like this: