R := Expand[1 + t12 + p2/2 + p3/6 + p4/24 + p5/120]
 
t12 = Graph[C1[2], C2[1]]
 
p2 = Graph[C1[2], C2[1]]^2 + Graph[C1[5], C2[6], Dashed[5, 6], Dashed[5, 6], 
     OV[1, 3, 4], OV[2, 3, 4]]/4
 
p3 = Graph[C1[2], C2[1]]^3 + (3*Graph[C1[2], C2[1]]*
      Graph[C1[5], C2[6], Dashed[5, 6], Dashed[5, 6], OV[1, 3, 4], 
       OV[2, 3, 4]])/4 - Graph[C1[6], C1[7], C2[7], C2[6], Dashed[6, 7], 
     OV[1, 4, 5], OV[2, 3, 5]]/2 + 
   Graph[C1[8], C2[9], Dashed[8, 10], Dashed[8, 10], Dashed[9, 11], 
     Dashed[9, 11], Dashed[10, 11], OV[1, 3, 4], OV[2, 5, 6], OV[3, 4, 7], 
     OV[5, 6, 7]]/12
 
p4 = Graph[C1[2], C2[1]]^4 + (3*Graph[C1[2], C2[1]]^2*
      Graph[C1[5], C2[6], Dashed[5, 6], Dashed[5, 6], OV[1, 3, 4], 
       OV[2, 3, 4]])/2 + (3*Graph[C1[5], C2[6], Dashed[5, 6], 
        Dashed[5, 6], OV[1, 3, 4], OV[2, 3, 4]]^2)/16 - 
   2*Graph[C1[2], C2[1]]*Graph[C1[6], C1[7], C2[7], C2[6], Dashed[6, 7], 
     OV[1, 4, 5], OV[2, 3, 5]] + 
   (Graph[C1[2], C2[1]]*Graph[C1[8], C2[9], Dashed[8, 10], Dashed[8, 10], 
       Dashed[9, 11], Dashed[9, 11], Dashed[10, 11], OV[1, 3, 4], 
       OV[2, 5, 6], OV[3, 4, 7], OV[5, 6, 7]])/3 + 
   (7*Graph[C1[11], C1[12], C2[10], C2[9], Dashed[11, 12], Dashed[10, 12], 
       Dashed[9, 11], Dashed[9, 10], OV[4, 7, 8], OV[3, 6, 8], OV[1, 5, 7], 
       OV[2, 5, 6]])/24 - (35*Graph[C1[11], C1[12], C2[12], C2[11], 
       Dashed[10, 12], Dashed[9, 11], Dashed[9, 10], Dashed[9, 10], 
       OV[6, 7, 8], OV[5, 7, 8], OV[1, 4, 6], OV[2, 3, 5]])/48 + 
   (5*Graph[C1[11], C2[12], Dashed[11, 13], Dashed[11, 13], Dashed[12, 16], 
       Dashed[12, 16], Dashed[15, 16], Dashed[13, 14], Dashed[14, 15], 
       Dashed[14, 15], OV[1, 3, 4], OV[2, 5, 6], OV[3, 4, 8], OV[8, 9, 10], 
       OV[7, 9, 10], OV[5, 6, 7]])/144
 
p5 = Graph[C1[2], C2[1]]^5 + (5*Graph[C1[2], C2[1]]^3*
      Graph[C1[5], C2[6], Dashed[5, 6], Dashed[5, 6], OV[1, 3, 4], 
       OV[2, 3, 4]])/2 + (15*Graph[C1[2], C2[1]]*
      Graph[C1[5], C2[6], Dashed[5, 6], Dashed[5, 6], OV[1, 3, 4], 
        OV[2, 3, 4]]^2)/16 - 5*Graph[C1[2], C2[1]]^2*
    Graph[C1[6], C1[7], C2[7], C2[6], Dashed[6, 7], OV[1, 4, 5], OV[2, 3, 5]]\
     - (5*Graph[C1[5], C2[6], Dashed[5, 6], Dashed[5, 6], OV[1, 3, 4], 
       OV[2, 3, 4]]*Graph[C1[6], C1[7], C2[7], C2[6], Dashed[6, 7], 
       OV[1, 4, 5], OV[2, 3, 5]])/4 + 
   (5*Graph[C1[2], C2[1]]^2*Graph[C1[8], C2[9], Dashed[8, 10], 
       Dashed[8, 10], Dashed[9, 11], Dashed[9, 11], Dashed[10, 11], 
       OV[1, 3, 4], OV[2, 5, 6], OV[3, 4, 7], OV[5, 6, 7]])/6 + 
   (5*Graph[C1[5], C2[6], Dashed[5, 6], Dashed[5, 6], OV[1, 3, 4], 
       OV[2, 3, 4]]*Graph[C1[8], C2[9], Dashed[8, 10], Dashed[8, 10], 
       Dashed[9, 11], Dashed[9, 11], Dashed[10, 11], OV[1, 3, 4], 
       OV[2, 5, 6], OV[3, 4, 7], OV[5, 6, 7]])/24 + 
   (35*Graph[C1[2], C2[1]]*Graph[C1[11], C1[12], C2[10], C2[9], 
       Dashed[11, 12], Dashed[10, 12], Dashed[9, 11], Dashed[9, 10], 
       OV[4, 7, 8], OV[3, 6, 8], OV[1, 5, 7], OV[2, 5, 6]])/24 - 
   (175*Graph[C1[2], C2[1]]*Graph[C1[11], C1[12], C2[12], C2[11], 
       Dashed[10, 12], Dashed[9, 11], Dashed[9, 10], Dashed[9, 10], 
       OV[6, 7, 8], OV[5, 7, 8], OV[1, 4, 6], OV[2, 3, 5]])/48 - 
   (13*Graph[C1[11], C1[13], C1[12], C2[10], C2[13], C2[12], 
       Dashed[10, 11], Dashed[10, 12], Dashed[11, 13], OV[4, 7, 8], 
       OV[1, 7, 9], OV[3, 6, 8], OV[2, 5, 9]])/6 - 
   Graph[C1[12], C1[13], C1[11], C1[10], C2[13], C2[12], Dashed[11, 13], 
     Dashed[10, 12], Dashed[10, 11], OV[4, 8, 9], OV[3, 7, 9], OV[1, 6, 8], 
     OV[2, 5, 7]]/3 - Graph[C1[12], C1[13], C2[13], C2[12], C2[11], C2[10], 
     Dashed[11, 13], Dashed[10, 12], Dashed[10, 11], OV[6, 8, 9], 
     OV[5, 7, 9], OV[1, 4, 8], OV[2, 3, 7]]/3 + 
   (25*Graph[C1[2], C2[1]]*Graph[C1[11], C2[12], Dashed[11, 13], 
       Dashed[11, 13], Dashed[12, 16], Dashed[12, 16], Dashed[15, 16], 
       Dashed[13, 14], Dashed[14, 15], Dashed[14, 15], OV[1, 3, 4], 
       OV[2, 5, 6], OV[3, 4, 8], OV[8, 9, 10], OV[7, 9, 10], OV[5, 6, 7]])/
    144 + (5*Graph[C1[12], C2[17], C2[15], C2[16], Dashed[12, 13], 
       Dashed[12, 13], Dashed[16, 17], Dashed[15, 17], Dashed[14, 16], 
       Dashed[14, 15], Dashed[13, 14], OV[1, 5, 6], OV[5, 6, 11], 
       OV[9, 10, 11], OV[3, 8, 10], OV[4, 7, 9], OV[2, 7, 8]])/48 - 
   (31*Graph[C1[16], C1[17], C2[14], C2[15], Dashed[14, 15], 
       Dashed[13, 17], Dashed[12, 17], Dashed[13, 16], Dashed[12, 16], 
       Dashed[13, 15], Dashed[12, 14], OV[7, 9, 11], OV[6, 8, 10], 
       OV[3, 5, 11], OV[4, 5, 10], OV[1, 8, 9], OV[2, 6, 7]])/144 - 
   (241*Graph[C1[16], C1[17], C2[15], C2[14], Dashed[14, 15], 
       Dashed[12, 17], Dashed[12, 17], Dashed[13, 16], Dashed[13, 16], 
       Dashed[13, 15], Dashed[12, 14], OV[6, 7, 11], OV[8, 9, 10], 
       OV[4, 5, 11], OV[3, 5, 10], OV[1, 8, 9], OV[2, 6, 7]])/288 + 
   (5*Graph[C1[17], C1[15], C1[16], C2[12], Dashed[12, 13], Dashed[12, 13], 
       Dashed[16, 17], Dashed[15, 17], Dashed[14, 16], Dashed[14, 15], 
       Dashed[13, 14], OV[4, 5, 6], OV[5, 6, 11], OV[9, 10, 11], 
       OV[2, 8, 10], OV[3, 7, 9], OV[1, 7, 8]])/48 + 
   (43*Graph[C1[17], C1[16], C2[15], C2[14], Dashed[15, 16], 
       Dashed[14, 15], Dashed[13, 17], Dashed[13, 17], Dashed[12, 16], 
       Dashed[12, 14], Dashed[12, 13], OV[9, 10, 11], OV[7, 8, 11], 
       OV[4, 6, 10], OV[3, 5, 6], OV[2, 5, 9], OV[1, 7, 8]])/72 + 
   (17*Graph[C1[14], C2[15], Dashed[14, 16], Dashed[14, 16], 
       Dashed[15, 21], Dashed[15, 21], Dashed[18, 21], Dashed[16, 17], 
       Dashed[18, 19], Dashed[18, 19], Dashed[17, 20], Dashed[17, 20], 
       Dashed[19, 20], OV[1, 3, 4], OV[2, 5, 6], OV[3, 4, 8], 
       OV[8, 11, 12], OV[7, 9, 10], OV[9, 10, 13], OV[11, 12, 13], 
       OV[5, 6, 7]])/960 - Graph[C1[14], C2[15], Dashed[14, 17], 
     Dashed[14, 16], Dashed[15, 21], Dashed[15, 20], Dashed[16, 20], 
     Dashed[17, 19], Dashed[17, 18], Dashed[16, 19], Dashed[19, 21], 
     Dashed[18, 21], Dashed[18, 20], OV[1, 3, 4], OV[2, 5, 6], OV[4, 7, 10], 
     OV[3, 8, 9], OV[9, 12, 13], OV[8, 10, 11], OV[6, 7, 13], OV[5, 11, 12]]/
    120
