# edge lists Edges[id]=[e1,...,e12] for all 288 automorphism classes of connected graphs with 12 edges, 7 vertices, and at least 3 edges incident to any vertex, and no odd automorphisms
# the edges ek=[u,v] are considered as directed from vertex u to vertex v for the purpose of defining the orientation of the graph (edge directions together with the vertex ordering 0<1<2<3<4<5<6)

Edges[1]:=[[0,6],[0,6],[0,6],[1,4],[1,4],[1,6],[2,5],[2,6],[2,6],[3,4],[3,5],[3,5]];
Edges[2]:=[[0,6],[0,6],[0,6],[1,4],[1,4],[1,6],[2,5],[2,5],[2,6],[3,4],[3,4],[3,5]];
Edges[3]:=[[0,6],[0,6],[0,6],[1,3],[1,3],[1,6],[2,4],[2,4],[2,6],[3,5],[4,5],[5,6]];
Edges[4]:=[[0,4],[0,4],[0,4],[1,5],[1,5],[1,6],[2,5],[2,6],[2,6],[3,4],[3,6],[3,6]];
Edges[5]:=[[0,4],[0,4],[0,4],[1,5],[1,5],[1,6],[2,5],[2,6],[2,6],[3,4],[3,4],[3,6]];
Edges[6]:=[[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,5],[3,5],[3,6],[4,5],[4,6],[4,6]];
Edges[7]:=[[0,5],[0,5],[0,6],[1,5],[1,6],[1,6],[2,3],[2,3],[2,6],[3,4],[4,5],[4,6]];
Edges[8]:=[[0,3],[0,3],[0,3],[1,4],[1,4],[1,4],[2,5],[2,5],[2,5],[3,6],[4,6],[5,6]];
Edges[9]:=[[0,5],[0,5],[0,5],[1,6],[1,6],[1,6],[2,3],[2,3],[2,4],[3,5],[4,6],[4,6]];
Edges[10]:=[[0,6],[0,6],[0,6],[1,4],[1,4],[1,4],[2,3],[2,3],[2,6],[3,5],[4,5],[5,6]];
Edges[11]:=[[0,3],[0,3],[0,3],[1,4],[1,4],[1,4],[2,5],[2,5],[2,6],[3,5],[4,6],[5,6]];
Edges[12]:=[[0,1],[0,1],[0,1],[1,6],[2,4],[2,6],[2,6],[3,5],[3,6],[3,6],[4,5],[4,5]];
Edges[13]:=[[0,1],[0,1],[0,1],[1,6],[2,4],[2,4],[2,6],[3,5],[3,6],[3,6],[4,5],[4,5]];
Edges[14]:=[[0,1],[0,1],[0,1],[1,6],[2,4],[2,4],[2,6],[3,5],[3,5],[3,6],[4,5],[4,5]];
Edges[15]:=[[0,1],[0,1],[0,1],[1,6],[2,4],[2,4],[2,6],[2,6],[3,5],[3,5],[3,6],[4,5]];
Edges[16]:=[[0,1],[0,1],[0,1],[1,6],[2,4],[2,4],[2,4],[2,6],[3,5],[3,5],[3,6],[4,5]];
Edges[17]:=[[0,4],[0,4],[0,4],[1,5],[1,5],[1,6],[2,3],[2,6],[2,6],[3,6],[3,6],[4,5]];
Edges[18]:=[[0,4],[0,4],[0,4],[1,5],[1,5],[1,6],[2,3],[2,3],[2,6],[2,6],[3,6],[4,5]];
Edges[19]:=[[0,4],[0,4],[0,4],[1,5],[1,5],[1,6],[2,3],[2,3],[2,3],[2,6],[3,6],[4,5]];
Edges[20]:=[[0,3],[0,3],[0,3],[1,4],[1,4],[1,6],[2,5],[2,6],[2,6],[3,6],[4,5],[5,6]];
Edges[21]:=[[0,3],[0,3],[0,3],[1,4],[1,4],[1,6],[2,5],[2,5],[2,6],[3,6],[4,5],[5,6]];
Edges[22]:=[[0,1],[0,1],[0,5],[1,6],[2,3],[2,6],[2,6],[3,5],[3,5],[4,5],[4,5],[4,6]];
Edges[23]:=[[0,1],[0,1],[0,5],[1,6],[2,3],[2,3],[2,6],[3,5],[4,5],[4,5],[4,5],[4,6]];
Edges[24]:=[[0,1],[0,1],[0,5],[0,5],[1,6],[2,3],[2,3],[2,6],[3,5],[4,5],[4,6],[4,6]];
Edges[25]:=[[0,1],[0,1],[0,5],[0,5],[1,6],[2,3],[2,3],[2,6],[3,5],[4,5],[4,5],[4,6]];
Edges[26]:=[[0,1],[0,1],[0,1],[0,5],[1,6],[2,3],[2,3],[2,6],[3,5],[4,5],[4,5],[4,6]];
Edges[27]:=[[0,5],[0,6],[0,6],[1,3],[1,3],[1,6],[2,4],[2,6],[2,6],[3,5],[4,5],[4,6]];
Edges[28]:=[[0,5],[0,6],[0,6],[1,3],[1,3],[1,6],[2,4],[2,4],[2,6],[3,5],[4,5],[4,6]];
Edges[29]:=[[0,5],[0,5],[0,6],[1,3],[1,3],[1,6],[2,4],[2,6],[2,6],[3,5],[4,5],[4,6]];
Edges[30]:=[[0,5],[0,5],[0,6],[1,3],[1,3],[1,6],[2,4],[2,4],[2,6],[3,5],[4,5],[4,6]];
Edges[31]:=[[0,1],[0,1],[0,5],[1,6],[2,3],[2,3],[2,6],[3,5],[4,5],[4,5],[4,6],[5,6]];
Edges[32]:=[[0,6],[0,6],[0,6],[1,2],[1,2],[1,6],[2,5],[3,4],[3,5],[3,6],[4,5],[4,6]];
Edges[33]:=[[0,2],[0,2],[0,2],[1,5],[1,6],[1,6],[2,6],[3,4],[3,5],[3,6],[4,5],[4,6]];
Edges[34]:=[[0,2],[0,2],[0,2],[1,5],[1,5],[1,6],[2,6],[3,4],[3,5],[3,6],[4,5],[4,6]];
Edges[35]:=[[0,1],[0,1],[0,5],[1,6],[2,5],[2,5],[2,6],[3,4],[3,5],[3,6],[4,5],[4,6]];
Edges[36]:=[[0,1],[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,4],[3,4],[3,5],[3,5],[4,6]];
Edges[37]:=[[0,1],[0,1],[0,1],[0,2],[0,2],[1,5],[2,6],[3,4],[3,5],[3,5],[4,6],[4,6]];
Edges[38]:=[[0,4],[0,4],[0,4],[1,4],[1,6],[1,6],[2,3],[2,3],[2,6],[3,5],[4,5],[5,6]];
Edges[39]:=[[0,4],[0,4],[0,4],[1,4],[1,4],[1,6],[2,3],[2,3],[2,6],[3,5],[4,5],[5,6]];
Edges[40]:=[[0,1],[0,1],[0,1],[1,4],[2,4],[2,6],[2,6],[3,5],[3,6],[3,6],[4,5],[5,6]];
Edges[41]:=[[0,1],[0,1],[0,1],[1,4],[2,4],[2,6],[2,6],[3,5],[3,5],[3,6],[4,5],[5,6]];
Edges[42]:=[[0,1],[0,1],[0,1],[1,4],[2,4],[2,4],[2,6],[3,5],[3,6],[3,6],[4,5],[5,6]];
Edges[43]:=[[0,1],[0,1],[0,1],[1,4],[2,4],[2,4],[2,6],[3,5],[3,5],[3,6],[4,5],[5,6]];
Edges[44]:=[[0,1],[0,2],[0,2],[1,3],[1,3],[2,5],[3,6],[4,5],[4,5],[4,6],[5,6],[5,6]];
Edges[45]:=[[0,1],[0,2],[0,2],[1,3],[1,3],[2,5],[3,6],[4,5],[4,5],[4,5],[4,6],[5,6]];
Edges[46]:=[[0,1],[0,2],[0,2],[1,3],[1,3],[2,5],[2,5],[3,6],[4,5],[4,6],[4,6],[5,6]];
Edges[47]:=[[0,1],[0,2],[0,2],[1,3],[1,3],[2,5],[2,5],[3,6],[4,5],[4,5],[4,6],[5,6]];
Edges[48]:=[[0,1],[0,2],[0,2],[0,2],[1,3],[1,3],[2,5],[3,6],[4,5],[4,6],[4,6],[5,6]];
Edges[49]:=[[0,1],[0,2],[0,2],[0,2],[1,3],[1,3],[2,5],[3,6],[4,5],[4,5],[4,6],[5,6]];
Edges[50]:=[[0,1],[0,1],[0,2],[1,3],[2,5],[2,5],[3,6],[3,6],[4,5],[4,5],[4,6],[5,6]];
Edges[51]:=[[0,1],[0,1],[0,2],[0,2],[1,3],[2,5],[3,6],[3,6],[4,5],[4,6],[4,6],[5,6]];
Edges[52]:=[[0,1],[0,1],[0,2],[0,2],[1,3],[2,5],[3,6],[3,6],[4,5],[4,5],[4,6],[5,6]];
Edges[53]:=[[0,1],[0,1],[0,2],[0,2],[1,3],[1,3],[2,5],[3,6],[4,5],[4,5],[4,6],[5,6]];
Edges[54]:=[[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,4],[3,5],[3,5],[4,6],[4,6],[5,6]];
Edges[55]:=[[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,4],[3,4],[3,5],[4,6],[5,6],[5,6]];
Edges[56]:=[[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,4],[3,4],[3,5],[4,6],[4,6],[5,6]];
Edges[57]:=[[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,4],[3,4],[3,5],[3,5],[4,6],[5,6]];
Edges[58]:=[[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,4],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[59]:=[[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[2,6],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[60]:=[[0,1],[0,1],[0,2],[1,5],[1,5],[2,6],[2,6],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[61]:=[[0,1],[0,1],[0,2],[0,2],[1,5],[2,6],[3,4],[3,4],[3,5],[3,5],[4,6],[5,6]];
Edges[62]:=[[0,1],[0,1],[0,2],[0,2],[1,5],[1,5],[2,6],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[63]:=[[0,1],[0,1],[0,1],[0,2],[1,5],[2,6],[2,6],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[64]:=[[0,1],[0,1],[0,1],[0,2],[0,2],[1,5],[2,6],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[65]:=[[0,2],[0,2],[0,2],[1,6],[1,6],[1,6],[2,3],[3,4],[3,5],[4,5],[4,6],[5,6]];
Edges[66]:=[[0,4],[0,4],[0,4],[1,2],[1,2],[1,3],[2,5],[3,6],[3,6],[4,5],[4,6],[5,6]];
Edges[67]:=[[0,1],[0,1],[0,1],[1,4],[2,3],[2,5],[2,5],[3,6],[3,6],[4,5],[4,6],[5,6]];
Edges[68]:=[[0,1],[0,1],[0,1],[1,4],[2,3],[2,3],[2,5],[3,6],[4,5],[4,6],[5,6],[5,6]];
Edges[69]:=[[0,1],[0,1],[0,1],[1,4],[2,3],[2,3],[2,5],[3,6],[4,5],[4,5],[4,6],[5,6]];
Edges[70]:=[[0,1],[0,1],[0,1],[1,4],[2,3],[2,3],[2,5],[2,5],[3,6],[4,5],[4,6],[5,6]];
Edges[71]:=[[0,1],[0,1],[0,1],[1,4],[2,3],[2,3],[2,3],[2,5],[3,6],[4,5],[4,6],[5,6]];
Edges[72]:=[[0,4],[0,4],[0,4],[1,2],[1,2],[1,4],[2,6],[3,5],[3,6],[3,6],[4,5],[5,6]];
Edges[73]:=[[0,4],[0,4],[0,4],[1,2],[1,2],[1,4],[2,6],[3,5],[3,5],[3,6],[4,5],[5,6]];
Edges[74]:=[[0,4],[0,6],[0,6],[1,2],[1,2],[1,6],[2,5],[3,4],[3,5],[3,5],[4,6],[5,6]];
Edges[75]:=[[0,4],[0,6],[0,6],[1,2],[1,2],[1,6],[2,5],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[76]:=[[0,4],[0,4],[0,6],[1,2],[1,2],[1,6],[2,5],[3,4],[3,5],[3,5],[4,6],[5,6]];
Edges[77]:=[[0,4],[0,4],[0,6],[1,2],[1,2],[1,6],[2,5],[3,4],[3,4],[3,5],[4,6],[5,6]];
Edges[78]:=[[0,5],[0,5],[0,5],[1,2],[1,2],[1,6],[2,3],[3,4],[3,6],[4,5],[4,6],[5,6]];
Edges[79]:=[[0,2],[0,2],[0,2],[1,5],[1,6],[1,6],[2,3],[3,4],[3,6],[4,5],[4,6],[5,6]];
Edges[80]:=[[0,2],[0,2],[0,2],[1,5],[1,5],[1,6],[2,3],[3,4],[3,6],[4,5],[4,6],[5,6]];
Edges[81]:=[[0,4],[0,6],[0,6],[1,3],[1,6],[1,6],[2,3],[2,3],[2,5],[4,5],[4,6],[5,6]];
Edges[82]:=[[0,4],[0,6],[0,6],[1,3],[1,3],[1,6],[2,3],[2,5],[2,5],[4,5],[4,6],[5,6]];
Edges[83]:=[[0,4],[0,6],[0,6],[1,3],[1,3],[1,6],[2,3],[2,3],[2,5],[4,5],[4,6],[5,6]];
Edges[84]:=[[0,4],[0,4],[0,6],[1,3],[1,6],[1,6],[2,3],[2,3],[2,5],[4,5],[4,6],[5,6]];
Edges[85]:=[[0,4],[0,4],[0,6],[1,3],[1,3],[1,6],[2,3],[2,5],[2,5],[4,5],[4,6],[5,6]];
Edges[86]:=[[0,4],[0,4],[0,6],[1,3],[1,3],[1,6],[2,3],[2,3],[2,5],[4,5],[4,6],[5,6]];
Edges[87]:=[[0,2],[0,2],[0,6],[1,3],[1,6],[1,6],[2,4],[3,5],[3,5],[4,5],[4,6],[5,6]];
Edges[88]:=[[0,2],[0,2],[0,6],[1,3],[1,3],[1,6],[2,4],[3,5],[4,5],[4,6],[4,6],[5,6]];
Edges[89]:=[[0,2],[0,2],[0,6],[1,3],[1,3],[1,6],[2,4],[2,4],[3,5],[4,5],[4,6],[5,6]];
Edges[90]:=[[0,2],[0,2],[0,6],[0,6],[1,3],[1,3],[1,6],[2,4],[3,5],[4,5],[4,6],[5,6]];
Edges[91]:=[[0,2],[0,2],[0,2],[0,6],[1,3],[1,3],[1,6],[2,4],[3,5],[4,5],[4,6],[5,6]];
Edges[92]:=[[0,4],[0,4],[0,6],[1,5],[1,6],[1,6],[2,3],[2,3],[2,4],[3,5],[4,6],[5,6]];
Edges[93]:=[[0,2],[0,2],[0,6],[1,4],[1,6],[1,6],[2,3],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[94]:=[[0,2],[0,2],[0,6],[1,4],[1,4],[1,6],[2,3],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[95]:=[[0,4],[0,4],[0,4],[1,2],[1,2],[1,5],[2,6],[3,5],[3,5],[3,6],[4,5],[4,6]];
Edges[96]:=[[0,6],[0,6],[0,6],[1,2],[1,2],[1,4],[2,5],[3,4],[3,5],[3,6],[4,6],[5,6]];
Edges[97]:=[[0,4],[0,4],[0,6],[1,5],[1,6],[1,6],[2,3],[2,4],[2,6],[3,5],[3,6],[4,5]];
Edges[98]:=[[0,6],[0,6],[0,6],[1,2],[1,4],[1,6],[2,5],[2,6],[3,4],[3,5],[3,6],[4,5]];
Edges[99]:=[[0,3],[0,5],[0,5],[1,4],[1,6],[1,6],[2,5],[2,5],[2,6],[3,4],[3,6],[4,5]];
Edges[100]:=[[0,3],[0,3],[0,5],[1,4],[1,6],[1,6],[2,5],[2,6],[2,6],[3,4],[3,6],[4,5]];
Edges[101]:=[[0,3],[0,3],[0,5],[1,4],[1,6],[1,6],[2,5],[2,5],[2,6],[3,4],[3,6],[4,5]];
Edges[102]:=[[0,3],[0,3],[0,5],[1,4],[1,4],[1,6],[2,5],[2,5],[2,6],[3,4],[3,6],[4,5]];
Edges[103]:=[[0,5],[0,6],[0,6],[1,3],[1,4],[1,4],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[104]:=[[0,5],[0,6],[0,6],[1,3],[1,3],[1,4],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[105]:=[[0,5],[0,5],[0,6],[1,3],[1,4],[1,4],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[106]:=[[0,5],[0,5],[0,6],[1,3],[1,3],[1,4],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[107]:=[[0,5],[0,6],[0,6],[1,4],[1,5],[1,5],[2,3],[2,5],[2,6],[3,4],[3,6],[4,6]];
Edges[108]:=[[0,5],[0,6],[0,6],[1,4],[1,4],[1,5],[2,3],[2,5],[2,6],[3,4],[3,6],[4,6]];
Edges[109]:=[[0,5],[0,5],[0,6],[1,4],[1,5],[1,5],[2,3],[2,5],[2,6],[3,4],[3,6],[4,6]];
Edges[110]:=[[0,5],[0,5],[0,6],[1,4],[1,4],[1,5],[2,3],[2,5],[2,6],[3,4],[3,6],[4,6]];
Edges[111]:=[[0,5],[0,5],[0,6],[1,2],[1,2],[1,3],[2,4],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[112]:=[[0,5],[0,5],[0,6],[1,2],[1,3],[1,5],[2,4],[2,6],[3,5],[3,6],[4,5],[4,6]];
Edges[113]:=[[0,1],[0,1],[0,1],[1,4],[2,5],[2,5],[2,6],[3,5],[3,6],[3,6],[4,5],[4,6]];
Edges[114]:=[[0,1],[0,1],[0,2],[1,5],[2,5],[2,5],[3,4],[3,6],[3,6],[4,6],[4,6],[5,6]];
Edges[115]:=[[0,1],[0,1],[0,2],[1,5],[2,5],[2,5],[3,4],[3,4],[3,6],[3,6],[4,6],[5,6]];
Edges[116]:=[[0,1],[0,1],[0,2],[1,5],[2,5],[2,5],[3,4],[3,4],[3,4],[3,6],[4,6],[5,6]];
Edges[117]:=[[0,1],[0,1],[0,1],[1,6],[2,3],[2,3],[2,4],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[118]:=[[0,3],[0,3],[0,4],[1,2],[1,2],[1,5],[2,6],[3,5],[3,6],[4,5],[4,5],[4,6]];
Edges[119]:=[[0,3],[0,3],[0,4],[1,2],[1,2],[1,5],[2,6],[3,5],[3,5],[3,6],[4,5],[4,6]];
Edges[120]:=[[0,3],[0,3],[0,4],[1,2],[1,2],[1,5],[1,5],[2,6],[3,5],[3,6],[4,5],[4,6]];
Edges[121]:=[[0,3],[0,3],[0,3],[0,4],[1,2],[1,2],[1,5],[2,6],[3,5],[3,6],[4,5],[4,6]];
Edges[122]:=[[0,5],[0,5],[0,5],[1,2],[1,3],[1,3],[2,5],[2,6],[3,4],[3,6],[4,5],[4,6]];
Edges[123]:=[[0,5],[0,5],[0,5],[1,2],[1,2],[1,3],[2,5],[2,6],[3,4],[3,6],[4,5],[4,6]];
Edges[124]:=[[0,1],[0,1],[0,1],[1,2],[2,3],[2,4],[3,5],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[125]:=[[0,1],[0,1],[0,1],[1,2],[2,3],[2,3],[2,4],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[126]:=[[0,3],[0,3],[0,4],[1,5],[1,5],[1,6],[2,5],[2,6],[2,6],[3,4],[3,5],[4,6]];
Edges[127]:=[[0,2],[0,6],[0,6],[1,3],[1,3],[1,4],[2,5],[2,6],[3,5],[3,6],[4,5],[4,6]];
Edges[128]:=[[0,2],[0,2],[0,6],[1,3],[1,3],[1,4],[2,5],[2,6],[3,5],[3,6],[4,5],[4,6]];
Edges[129]:=[[0,3],[0,6],[0,6],[1,4],[1,5],[1,5],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[130]:=[[0,3],[0,6],[0,6],[1,4],[1,4],[1,5],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[131]:=[[0,3],[0,3],[0,6],[1,4],[1,5],[1,5],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[132]:=[[0,3],[0,3],[0,6],[1,4],[1,4],[1,5],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]];
Edges[133]:=[[0,1],[0,1],[0,6],[1,5],[2,4],[2,5],[2,6],[2,6],[3,4],[3,5],[3,6],[4,6]];
Edges[134]:=[[0,1],[0,1],[0,6],[1,5],[2,4],[2,5],[2,5],[2,6],[3,4],[3,5],[3,6],[4,6]];
Edges[135]:=[[0,1],[0,1],[0,6],[1,5],[2,4],[2,4],[2,5],[2,6],[3,4],[3,5],[3,6],[4,6]];
Edges[136]:=[[0,1],[0,1],[0,5],[1,4],[2,3],[2,6],[2,6],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[137]:=[[0,1],[0,1],[0,5],[1,4],[2,3],[2,3],[2,6],[3,5],[3,6],[4,5],[4,6],[5,6]];
Edges[138]:=[[0,3],[0,3],[0,4],[1,2],[1,5],[1,5],[2,6],[2,6],[3,4],[3,5],[4,6],[5,6]];
Edges[139]:=[[0,3],[0,3],[0,4],[1,2],[1,2],[1,5],[2,6],[3,4],[3,5],[4,6],[5,6],[5,6]];
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