File:Graph homomorphism into C5.svg
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Original file (SVG file, nominally 259 × 460 pixels, file size: 34 KB)
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Summary
| Description |
English: A homomorphism from the flower snark J5 to the cycle graph C5. It is also a retraction onto the subgraph on the central five vertices, so J5 is in fact homomorphically equivalent to core graph C5. |
| Date | |
| Source | Own work |
| Author | Tokenzero |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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LaTeX/TikZ source code
\documentclass[tikz,border=10pt]{standalone}
%% Compile svg by running:
%% latex example.tex #OR: lualatex --output-format=dvi example.tex
%% dvisvgm --bbox=10 example.dvi
\usepackage{tikz}
\usetikzlibrary{calc}
\definecolor{col0}{RGB}{255, 51, 51}
\definecolor{col1}{RGB}{215,255, 51}
\definecolor{col2}{RGB}{ 51,255,133}
\definecolor{col3}{RGB}{ 51,133,255}
\definecolor{col4}{RGB}{215, 51,255}
\begin{document}%
\begin{tikzpicture}[
scale=0.8,rotate=90,every node/.style={draw,circle},
C0/.style={fill=col0},
C1/.style={fill=col1},
C2/.style={fill=col2},
C3/.style={fill=col3},
C4/.style={fill=col4}
]
%the flower snark graph J_5
%vertices
\foreach \x/\c in {0/4, 1/3, 2/2, 3/1, 4/0}
\node[C\c] (u\x) at (\x * 72 :1.5) {\c};
\foreach \x/\c in {0/0, 1/4, 2/3, 3/4, 4/3, 5/2, 6/3, 7/2, 8/1, 9/2, 10/1, 11/0, 12/1, 13/0, 14/4}
\node[C\c] (v\x) at (\x * 24 :3.75) {\c};
%edges
\foreach \x in {0,...,4}
{
\pgfmathtruncatemacro{\xp}{mod(\x+1,5)};
\draw (u\x) -- (u\xp);
\pgfmathtruncatemacro{\xx}{3*\x};
\draw (u\x) -- (v\xx);
\pgfmathtruncatemacro{\xa}{3*\x+1};
\pgfmathtruncatemacro{\xb}{mod(3*\x+11,15)};
\draw (v\xa) -- (v\xb);
}
\foreach \x in {0,...,14}
{
\pgfmathtruncatemacro{\xp}{mod(\x+1,15)};
\draw (v\x) -- (v\xp);
}
%the image of J_5 in C_5
\begin{scope}[shift={(-8,0)}]
%blob edges
\foreach \x in {0,...,4}
{
\pgfmathtruncatemacro{\xp}{mod(\x+1,5)};
\draw[gray!15!white,line width=40pt](\x * 72 :2.6) -- (\xp * 72 :2.7);
}
%blobs
\foreach \x/\c in {0/4, 1/3, 2/2, 3/1, 4/0}
\node[draw=none,fill=col\c!30!white,minimum size=50pt] (u\x) at (\x * 72 :2.6) {};
%vertices
\foreach \x/\c in {0/4, 1/3, 2/2, 3/1, 4/0}
\node[C\c] (u\x) at (\x * 72 :2) {};
\foreach \x/\c/\d in {0/0/2, 1/4/0, 2/3/0, 3/4/2, 4/3/1, 5/2/0, 6/3/2, 7/2/1, 8/1/0, 9/2/2, 10/1/1, 11/0/1, 12/1/2, 13/0/0, 14/4/1}
\node[C\c] (v\x) at ((-72 - \c * 72 + \d*12-12 :3) {};
%the same edges
\foreach \x in {0,...,4}
{
\pgfmathtruncatemacro{\xp}{mod(\x+1,5)};
\draw (u\x) -- (u\xp);
\pgfmathtruncatemacro{\xx}{3*\x};
\draw (u\x) -- (v\xx);
\pgfmathtruncatemacro{\xa}{3*\x+1};
\pgfmathtruncatemacro{\xb}{mod(3*\x+11,15)};
\draw (v\xa) -- (v\xb);
}
\foreach \x in {0,...,14}
{
\pgfmathtruncatemacro{\xp}{mod(\x+1,15)};
\draw (v\x) -- (v\xp);
}
\end{scope}
\end{tikzpicture}%
\end{document}
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:55, 4 April 2017 | | 259 × 460 (34 KB) | wikimediacommons>Tokenzero | Highlight C5 as blobs. |
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