Vtyjkyuk

I want to make tree with each node has valency of three. I got the below code online somewhere. The first level has valency three however second and third level has valency four, and I also want to color the child different from parent and just want to use three colors. (e.g if parent is red then the branches will be green and blue)

documentclassminimal
usepackagetikz
usetikzlibrarytrees,snakes
begindocument
pagestyleempty
tikzstylelevel 1=[level distance= 32mm,sibling angle=120]
tikzstylelevel 2=[level distance= 16mm,sibling angle=60]
tikzstylelevel 3=[level distance = 12mm,sibling angle=30]
tikzstyleevery node=[fill]
%tikzstyleedge from parent=[segment length=1mm,
% segment angle=10,draw]
begintikzpicture[grow cyclic,shape=circle,very thick,level distance=13mm,
 cap=round]
node child [color=A] foreach A in red,green,blue
 node child [color=A!50!B] foreach B in red, green,blue
 node child [color=A!50!B!50!C] foreach C in red,green,blue
 node 
 
 ;
endtikzpicture

I am new in using tikz and didn't feel comfortable in working with it so far.

Very similar to Andrew's nice answer except that parents and children have different colors. EDIT: removed a superfluous index, big thanks to Andrew! @nd EDIT: Simplification with pgfkeysalso.

documentclass[tikz,border=3.14mm]standalone
usetikzlibrarytrees,snakes
begindocument
pagestyleempty
xdefmycolorblack
xdefColorList"red","green!60!black","blue"
tikzsetlevel 1/.style=level distance= 32mm,sibling angle=120,
level 2/.style=level distance= 16mm,sibling angle=60,
level 3/.style=level distance = 12mm,sibling angle=30,
every node/.append style=fill,
my color/.code=pgfmathparseColorList[mod(#1,3)]
pgfkeysalso/tikz/color/.expanded=pgfmathresult
begintikzpicture[grow cyclic,shape=circle,very thick,level distance=13mm,
 cap=round]
node child [my color=A] foreach A in 0,1,2
 node child [my color=A+B+1] foreach B in 0,1
 node child [my color=A+B+C+2] foreach C in 0,1
 node 
 
 ;
endtikzpicture
enddocument 

If you want each vertex to have valence 3 then you should loop over only two colours for the child nodes. This produces:

Here is the modified code:

documentclassminimal
usepackagetikz
usetikzlibrarytrees,snakes
begindocument
pagestyleempty
tikzstylelevel 1=[level distance= 32mm,sibling angle=120]
tikzstylelevel 2=[level distance= 16mm,sibling angle=60]
tikzstylelevel 3=[level distance = 12mm,sibling angle=30]
tikzstyleevery node=[fill]
%tikzstyleedge from parent=[segment length=1mm,
% segment angle=10,draw]
begintikzpicture[grow cyclic,shape=circle,very thick,level distance=13mm,
 cap=round]
node child [color=A] foreach A in red,green,blue
 node child [color=A!50!B] foreach B in red, green
 node child [color=A!50!B!50!C] foreach C in red,green
 node 
 
 ;
endtikzpicture

enddocument