<< DiscreteMath`Combinatorica`
<< Graphics`Animation`

\(Euler[x_Graph]\  := \ 
      Module[{\ data\  = \ x, \ el}, \ eulerList\  = \ EulerianCycle[x]; \ 
        el\  = \ Partition[eulerList, \ 2, \ 
            1]; \ 
data\  = 
          SetGraphOptions[\ 
            data, \ {\ eulerList[\([1]\)], \ 
              VertexColor -> Green}]; 
eulerfile\  = \ 
          Table[
Show[\ 
Graphics[\ {
Rectangle[\ {0, 0}, \ {0.8, \ 
                      0.8}, 
ShowGraph[\ 
                      Highlight[\ 
                        data, \ {Take[el, \ Quotient[t, \ 2]], \ {\ 
                            eulerList[\([\ 
                                Quotient[t, \ 2]\  + \ 
                                  Mod[t, \ 
                                    2]]\)]\ }\ }, \ {HighlightedEdgeColors\  -> \ {Blue}, \ HighlightedVertexColors\  -> \ {Yellow}, \ 
                          HighlightedVertexStyle\  -> \ Disk[Normal]}], \ 
                      PlotLabel\  -> \ "Eulerian Cycle", \ 
                      TextStyle\  -> \ {FontSize\  -> \ 15, \ 
                          FontColor -> 
                            Purple}, 
Background -> 
                        RGBColor[1, 1, 1], 
\ 
                      Graphics\ ]], 
\ 
                  Text["www.combinatorica.com", \ {0.5, 
                      0.0}, \ {TextStyle -> {FontColor -> 
                            Red}}]\ }, 
{\ 
                  ImageSize -> 350, \ 
                  AspectRatio -> 
                    1}
\ ]
], \ {t, \ 
              1, \ 2*\((Length[eulerList]\  - \ 1)\), \ 
              1}]; \ 
eulerfile
]\)

\(\(\(ShowGraph[
      a\  = \ Graph[{{{1, 2}}, {{2, 3}}, {{3, 4}}, {{4, 5}}, {{5, 6}}, {{6, 
                7}}, {{7, 8}}, {{8, 9}}, {{9, 10}}, {{11, 12}}, {{12, 
                13}}, {{13, 14}}, {{14, 15}}, {{15, 16}}, {{16, 17}}, {{17, 
                18}}, {{18, 19}}, {{19, 20}}, {{21, 22}}, {{22, 23}}, {{23, 
                24}}, {{24, 25}}, {{25, 26}}, {{26, 27}}, {{27, 28}}, {{28, 
                29}}, {{29, 30}}, {{31, 32}}, {{32, 33}}, {{33, 34}}, {{34, 
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                104}}, {{60, 104}}, {{70, 104}}, {{80, 104}}, {{90, 
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                10. }}, {{10. , 10. }}, {{0, 5.5}}, {{5.5, 0}}, {{5.5, 
                11}}, {{11, 5.5}}}]]\)\(
\)
    \)\)

ShowAnimation[Euler[a]]