# File:Graph homomorphism into C5.svg Information

https://en.wikipedia.org/wiki/File:Graph_homomorphism_into_C5.svg

Original file(SVG file, nominally 259 × 460 pixels, file size: 34 KB)

## 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 18 March 2017 Source Own work Author Tokenzero

## Licensing

I, the copyright holder of this work, hereby publish it under the following license:
 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.

## 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}


# Information

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## File history

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Date/TimeThumbnailDimensionsUserComment
current 09:55, 4 April 2017 259 × 460 (34 KB)TokenzeroHighlight C5 as blobs.
16:31, 18 March 2017 259 × 453 (33 KB)TokenzeroImprove the lower layout.
16:15, 18 March 2017 259 × 452 (33 KB)TokenzeroRescale to make font bigger on thumb.
16:08, 18 March 2017 312 × 554 (34 KB)Tokenzero+margins
15:54, 18 March 2017 287 × 529 (34 KB)TokenzeroUser created page with UploadWizard
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