Problem with HighlightGraph

Questions
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1

Hi, everybody i have the follow problem , my graph has some vertices and I highlight the way that I get with the FindEulerianCycle command, but do not put it in red as usual, because it will not, here is my code

rutas = Graph[{1 \[UndirectedEdge] 12, 1 \[UndirectedEdge] 2, 
   2 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 9, 
   3 \[UndirectedEdge] 4, 3 \[UndirectedEdge] 8, 
   4 \[UndirectedEdge] 7, 4 \[UndirectedEdge] 5, 
   5 \[UndirectedEdge] 6, 6 \[UndirectedEdge] 8, 
   7 \[UndirectedEdge] 10, 8 \[UndirectedEdge] 9, 
   8 \[UndirectedEdge] 11, 3 \[UndirectedEdge] 9, 
   4 \[UndirectedEdge] 10, 9 \[UndirectedEdge] 11, 
   2 \[UndirectedEdge] 12}, VertexLabels -> "Name", 
  ImagePadding -> 10]

With this check if a graph is Eulerian

EulerianGraphQ[rutas]

Upon request from you, the program does the highlighted path in the graph

caminos = FindEulerianCycle[rutas]

HighlightGraph[rutas, PathGraph[First[caminos]

I hope something can help me find the solution, or tell me why that happens.

Thanks in advance

2

You are missing square parenthesis at the end of your last line. But that’s not the main error. PathGraph is - you should not use it, just use list of edges. Because you are interested in an edge path, you should label edges, not vertices:

rutas = Graph[{1 <-> 12, 1 <-> 2, 2 <-> 3, 2 <-> 9, 3 <-> 4, 3 <-> 8, 
    4 <-> 7, 4 <-> 5, 5 <-> 6, 6 <-> 8, 7 <-> 10, 8 <-> 9, 8 <-> 11, 
    3 <-> 9, 4 <-> 10, 9 <-> 11, 2 <-> 12}, ImagePadding -> 10];
caminos = First[FindEulerianCycle[rutas]];
HighlightGraph[rutas, Table[Labeled[caminos[[i]], i], {i, Length[caminos]}]]

we3frsdf32f4rfsddsf4356547.png
we3frsdf32f4rfsddsf4356547.png337×200 8.75 KB

3

Many thanks Sam, it was what I needed to understand