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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 …

 

 

Written by meditationatae

March 20, 2017 at 8:00 am

Posted in History

Image of a 15-vertex 35-edge possible unit distance graph

Scanudg15a

Written by meditationatae

March 18, 2017 at 10:54 pm

Posted in History

Using the ldd command with the verbose option

With respect to the readline library, some versions have various symbols (UP, etc.) defined, and some do not.

For PARI/gp on my system, it only works when these various symbols are defined.

 

PARI/gp question: how does one get a history of the commands input at the terminal ?

 

 

We are in the directory:  /usr/local/lib .

ls -l gives output:

-rw-r–r–. 1 root root 1291398 Feb 22 12:51 libgmp.a
-rwxr-xr-x. 1 root root 913 Feb 22 12:51 libgmp.la
lrwxrwxrwx. 1 root root 16 Feb 22 12:51 libgmp.so -> libgmp.so.10.3.2
lrwxrwxrwx. 1 root root 16 Feb 22 12:51 libgmp.so.10 -> libgmp.so.10.3.2
-rwxr-xr-x. 1 root root 523381 Feb 22 12:51 libgmp.so.10.3.2
-rw-r–r–. 1 root root 162874 Feb 23 02:55 libhistory.a
-rw-r–r–. 1 root root 171982 Feb 22 14:11 libhistory.old
lrwxrwxrwx. 1 root root 15 Feb 23 02:55 libhistory.so -> libhistory.so.6
lrwxrwxrwx. 1 root root 17 Feb 23 02:55 libhistory.so.6 -> libhistory.so.6.3
-r-xr-xr-x. 1 root root 99093 Feb 23 02:55 libhistory.so.6.3
lrwxrwxrwx. 1 root root 21 Feb 22 14:11 libhistory.so.7 -> libhistory.so.7.0.old
-r-xr-xr-x. 1 root root 106376 Feb 22 14:11 libhistory.so.7.0
-r-xr-xr-x. 1 root root 106376 Feb 22 12:35 libhistory.so.7.0.old
-rwxr-xr-x. 1 root root 7060519 Feb 23 11:55 libpari-gmp.so.2.9.1
lrwxrwxrwx. 1 root root 20 Feb 23 11:55 libpari-gmp.so.5 -> libpari-gmp.so.2.9.1
lrwxrwxrwx. 1 root root 20 Feb 23 11:55 libpari.so -> libpari-gmp.so.2.9.1
-rw-r–r–. 1 root root 1199592 Feb 23 02:55 libreadline.a
-rw-r–r–. 1 root root 1239926 Feb 22 14:11 libreadline.old
lrwxrwxrwx. 1 root root 16 Feb 23 02:55 libreadline.so -> libreadline.so.6
lrwxrwxrwx. 1 root root 25 Mar 10 08:32 libreadline.so.6 -> /lib64/libreadline.so.6.0
-r-xr-xr-x. 1 root root 680148 Feb 23 02:55 libreadline.so.6.3
lrwxrwxrwx. 1 root root 22 Feb 22 14:11 libreadline.so.7 -> libreadline.so.7.0.old
-r-xr-xr-x. 1 root root 702910 Feb 22 14:11 libreadline.so.7.0
-r-xr-xr-x. 1 root root 702910 Feb 22 12:35 libreadline.so.7.0.old
drwxr-xr-x. 2 root root 4096 Feb 23 11:55 pari

 

I single out the libreadline text:

lrwxrwxrwx. 1 root root 16 Feb 23 02:55 libreadline.so -> libreadline.so.6
lrwxrwxrwx. 1 root root 25 Mar 10 08:32 libreadline.so.6 -> /lib64/libreadline.so.6.0

 

The ‘l’ signifies a symbolic link, so that

libreadline.so is an alias name for libreadline.so.6, and

libreadline.so.6 is an alias name for /lib64/libreadline.so.6.0 , and

/lib64/libreadline.so.6.0 is a normal file:

$ ls -l /lib64/libreadline.so.6.0
-rwxr-xr-x. 1 root root 272008 Jun 22 2012 /lib64/libreadline.so.6.0    (272 kbytes ).

 

Now, I try:

$ ldd -v libreadline.so  and I get this:

 

linux-vdso.so.1 => (0x00007ffd3c5fc000)
libtinfo.so.5 => /lib64/libtinfo.so.5 (0x0000003b0fa00000)
libc.so.6 => /lib64/libc.so.6 (0x0000003afce00000)
/lib64/ld-linux-x86-64.so.2 (0x0000003afc600000)

Version information:
./libreadline.so:
libc.so.6 (GLIBC_2.4) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.3) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.3.4) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.11) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.2.5) => /lib64/libc.so.6
/lib64/libtinfo.so.5:
libc.so.6 (GLIBC_2.4) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.3) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.3.4) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.2.5) => /lib64/libc.so.6
/lib64/libc.so.6:
ld-linux-x86-64.so.2 (GLIBC_PRIVATE) => /lib64/ld-linux-x86-64.so.2
ld-linux-x86-64.so.2 (GLIBC_2.3) => /lib64/ld-linux-x86-64.so.2

 

Note: there are no missing symbols.

 

What about libreadline.so.6.3 ? It looks just as good…

 

$ ldd -v libreadline.so.6.3         gives output:

linux-vdso.so.1 => (0x00007ffdd6951000)
libc.so.6 => /lib64/libc.so.6 (0x00007f815ed7e000)
/lib64/ld-linux-x86-64.so.2 (0x0000003afc600000)

Version information:
./libreadline.so.6.3:
libc.so.6 (GLIBC_2.3) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.2.5) => /lib64/libc.so.6
/lib64/libc.so.6:
ld-linux-x86-64.so.2 (GLIBC_PRIVATE) => /lib64/ld-linux-x86-64.so.2
ld-linux-x86-64.so.2 (GLIBC_2.3) => /lib64/ld-linux-x86-64.so.2

===

It looks good too, although  /lib64/libtinfo.so.5 present in first is what defines UP etc.

 

===

Another try, this time with:  libreadline.so.7.0

 

$ ldd -v libreadline.so.7.0
linux-vdso.so.1 => (0x00007fff4e3b2000)
libc.so.6 => /lib64/libc.so.6 (0x00007f301dec9000)
/lib64/ld-linux-x86-64.so.2 (0x0000003afc600000)

Version information:
./libreadline.so.7.0:
libc.so.6 (GLIBC_2.3) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.2.5) => /lib64/libc.so.6
/lib64/libc.so.6:
ld-linux-x86-64.so.2 (GLIBC_PRIVATE) => /lib64/ld-linux-x86-64.so.2
ld-linux-x86-64.so.2 (GLIBC_2.3) => /lib64/ld-linux-x86-64.so.2

 

===

this one also doesn’t have

/lib64/libtinfo.so.5.

===

linux-vdso.so.1 => (0x00007ffe2756a000)
libc.so.6 => /lib64/libc.so.6 (0x0000003afce00000)
/lib64/ld-linux-x86-64.so.2 (0x0000003afc600000)

Version information:
/lib64/libtinfo.so.5:
libc.so.6 (GLIBC_2.4) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.3) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.3.4) => /lib64/libc.so.6
libc.so.6 (GLIBC_2.2.5) => /lib64/libc.so.6
/lib64/libc.so.6:
ld-linux-x86-64.so.2 (GLIBC_PRIVATE) => /lib64/ld-linux-x86-64.so.2
ld-linux-x86-64.so.2 (GLIBC_2.3) => /lib64/ld-linux-x86-64.so.2

===

Written by meditationatae

March 17, 2017 at 6:12 pm

Posted in History

Re: “Best candidate” graph, 14 vertices, udg

The post from a few weeks ago shows a 14-vertex 33-edge probable unit distance graph with 324 4-colorings.

The URL of that blog post =

https://meditationatae.wordpress.com/2017/02/20/best-candidate-graph-14-vertices-udg/

Written by meditationatae

March 14, 2017 at 2:46 pm

Posted in History

Figure of a 13-vertex 28-edge graph

It’s a probable unit distance graph.

It has 356 4-colorings, and is not 3-colorable.

Its adjacency matrix is:

0 0 0 0 0 0 0 0 1 0 0 1 1
0 0 0 0 0 1 0 1 1 1 0 0 1
0 0 0 1 0 1 0 0 1 0 1 0 0
0 0 1 0 0 0 1 1 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0 1 1 0
0 1 1 0 0 0 0 1 0 0 1 1 0
0 0 0 1 1 0 0 1 0 0 1 0 1
0 1 0 1 0 1 1 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 1
0 0 1 0 1 1 1 0 0 0 0 0 1
1 0 0 0 1 1 0 1 0 0 0 0 0
1 1 0 0 0 0 1 0 1 1 1 0 0

 

It also contains as a subgraph the Moser spindle; one of the vertices of the Moser spindle subgraph is the degree 4 (in the Moser spindle) vertex that is uppermost in the figure. Five of the seven vertices in the Moser spindle together with 5 edges amongst these 5 vertices make up a pentagon with bilateral symmetry; by staring enough at the figure, it can be found by me without too much trouble:

Graph13-12ed-Screenshot

Written by meditationatae

March 10, 2017 at 2:58 pm

Posted in History

My first test-drive using exiftool on Windows

I had read that EXIF metadata in files that are images, whether .jpg or other file formats, have embbedded data, sometimes inluding geotags (coordinates).

Below is the copy/paste of my first test running exiftool.exe on Windows 10:

C:\Users\abcde\Downloads> C:\Users\abcde\Downloads\exiftool -All Louvre_Museum_Wikimedia_Commons.jpg

ExifTool Version Number : 10.45
File Name : Louvre_Museum_Wikimedia_Commons.jpg
Directory : .
File Size : 53 kB
File Modification Date/Time : 2017:03:08 07:18:37-05:00
File Access Date/Time : 2017:03:08 07:18:37-05:00
File Creation Date/Time : 2017:03:08 07:18:36-05:00
File Permissions : rw-rw-rw-
File Type : JPEG
File Type Extension : jpg
MIME Type : image/jpeg
JFIF Version : 1.01
Resolution Unit : inches
X Resolution : 240
Y Resolution : 240
Comment : File source: https://commons.wikimedia.org/wiki/File:Louvre_Museum_Wikimedia_Commons.jpg
Profile CMM Type : lcms
Profile Version : 2.1.0
Profile Class : Display Device Profile
Color Space Data : RGB
Profile Connection Space : XYZ
Profile Date Time : 2012:01:25 03:41:57
Profile File Signature : acsp
Primary Platform : Apple Computer Inc.
CMM Flags : Not Embedded, Independent
Device Manufacturer :
Device Model :
Device Attributes : Reflective, Glossy, Positive, Color
Rendering Intent : Perceptual
Connection Space Illuminant : 0.9642 1 0.82491
Profile Creator : lcms
Profile ID : 0
Profile Description : c2
Profile Copyright : FB
Media White Point : 0.9642 1 0.82491
Media Black Point : 0.01205 0.0125 0.01031
Red Matrix Column : 0.43607 0.22249 0.01392
Green Matrix Column : 0.38515 0.71687 0.09708
Blue Matrix Column : 0.14307 0.06061 0.7141
Red Tone Reproduction Curve : (Binary data 64 bytes, use -b option to extract)
Green Tone Reproduction Curve : (Binary data 64 bytes, use -b option to extract)
Blue Tone Reproduction Curve : (Binary data 64 bytes, use -b option to extract)
Image Width : 800
Image Height : 336
Encoding Process : Baseline DCT, Huffman coding
Bits Per Sample : 8
Color Components : 3
Y Cb Cr Sub Sampling : YCbCr4:2:0 (2 2)
Image Size : 800×336
Megapixels : 0.269

Written by meditationatae

March 8, 2017 at 12:41 pm

Posted in History

A 12-vertex, 26-edge, probable unit distance graph

okmarch4scan

The 12-vertex, 26-edge graph shown above is not 3-colorable, and is 4-colorable in 178 ways, up to permutation of the four colors. Numerical evidence suggests that it is a unit distance graph, i.e. embeddable in the plane with all edges of unit length.

My unit distance graph solver found no 12-vertex, non 3-colorable, 4-colorable udg with less than 178 different colorings, counting permutations of the four colors as equivalent. The search was not exahaustive and lasted a day.

Below, I copy the adjacency matrix for the graph above. The rows and columns are not labeled, but it is easy to guess: A for row 1, B for row 2, C for row 3, …. L for row 12; similarly for the labeling of the columns.

I don’t know how to do a fixed-width, or monospace font, in WordPress, so I omit the labels to avoid misalignment.

Adjacency matrix, 12 by 12:

0 1 0 0 0 1 1 1 1 0 0 0
1 0 0 0 0 0 0 0 1 0 1 1
0 0 0 1 0 1 1 0 0 1 0 1
0 0 1 0 1 1 0 0 1 0 0 0
0 0 0 1 0 0 0 1 1 1 1 0
1 0 1 1 0 0 0 1 0 0 0 0
1 0 1 0 0 0 0 0 1 1 0 0
1 0 0 0 1 1 0 0 0 1 1 0
1 1 0 1 1 0 1 0 0 0 0 0
0 0 1 0 1 0 1 1 0 0 0 1
0 1 0 0 1 0 0 1 0 0 0 0
0 1 1 0 0 0 0 0 0 1 0 0

 

Written by meditationatae

March 4, 2017 at 8:28 pm

Posted in History