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Table of Contents - 21.50.15.8. Generalized Petersen graphs

According to Wikipedia "Generalized Petersen graph", 26-Aug-2025, https://en.wikipedia.org/wiki/Generalized_Petersen_graph: "In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. They include the Petersen graph and generalize one of the ways of constructing the Petersen graph. ... Among the generalized Petersen graphs are the n-prism, ...".

The vertices of the regular polygon are called "outside vertices", the vertices of the star polygon "inside vertices" (see A. Steimle, W. Stanton, "The isomorphism classes of the generalized Petersen graphs", Discrete Mathematics Volume 309, Issue 1, 6 January 2009, Pages 231-237: https://doi.org/10.1016/j.disc.2007.12.074). Since regular polygons are also considered as star polygons (with density 1), many theorems for "inside vertices" (with labels containing the fragment "vtx1") can be specialized for "outside vertices" (with labels containing the fragment "vtx0").

  1. cgpg
  2. df-gpg
  3. gpgov
  4. gpgvtx
  5. gpgiedg
  6. gpgedg
  7. gpgiedgdmellem
  8. gpgvtxel
  9. gpgvtxel2
  10. gpgiedgdmel
  11. gpgedgel
  12. gpgprismgriedgdmel
  13. gpgprismgriedgdmss
  14. gpgvtx0
  15. gpgvtx1
  16. opgpgvtx
  17. gpgusgralem
  18. gpgusgra
  19. gpgprismgrusgra
  20. gpgorder
  21. gpg5order
  22. gpgedgvtx0
  23. gpgedgvtx1
  24. gpgvtxedg0
  25. gpgvtxedg1
  26. gpgedgiov
  27. gpgedg2ov
  28. gpgedg2iv
  29. gpg5nbgrvtx03starlem1
  30. gpg5nbgrvtx03starlem2
  31. gpg5nbgrvtx03starlem3
  32. gpg5nbgrvtx13starlem1
  33. gpg5nbgrvtx13starlem2
  34. gpg5nbgrvtx13starlem3
  35. gpgnbgrvtx0
  36. gpgnbgrvtx1
  37. gpg3nbgrvtx0
  38. gpg3nbgrvtx0ALT
  39. gpg3nbgrvtx1
  40. gpgcubic
  41. gpg5nbgrvtx03star
  42. gpg5nbgr3star
  43. gpgvtxdg3
  44. gpg3kgrtriexlem1
  45. gpg3kgrtriexlem2
  46. gpg3kgrtriexlem3
  47. gpg3kgrtriexlem4
  48. gpg3kgrtriexlem5
  49. gpg3kgrtriexlem6
  50. gpg3kgrtriex
  51. gpg5gricstgr3
  52. pglem
  53. pgjsgr
  54. gpg5grlim
  55. gpg5grlic
  56. gpgprismgr4cycllem1
  57. gpgprismgr4cycllem2
  58. gpgprismgr4cycllem3
  59. gpgprismgr4cycllem4
  60. gpgprismgr4cycllem5
  61. gpgprismgr4cycllem6
  62. gpgprismgr4cycllem7
  63. gpgprismgr4cycllem8
  64. gpgprismgr4cycllem9
  65. gpgprismgr4cycllem10
  66. gpgprismgr4cycllem11
  67. gpgprismgr4cycl0
  68. gpgprismgr4cyclex
  69. pgnioedg1
  70. pgnioedg2
  71. pgnioedg3
  72. pgnioedg4
  73. pgnioedg5
  74. pgnbgreunbgrlem1
  75. pgnbgreunbgrlem2lem1
  76. pgnbgreunbgrlem2lem2
  77. pgnbgreunbgrlem2lem3
  78. pgnbgreunbgrlem2
  79. pgnbgreunbgrlem3
  80. pgnbgreunbgrlem4
  81. pgnbgreunbgrlem5lem1
  82. pgnbgreunbgrlem5lem2
  83. pgnbgreunbgrlem5lem3
  84. pgnbgreunbgrlem5
  85. pgnbgreunbgrlem6
  86. pgnbgreunbgr
  87. pgn4cyclex
  88. pg4cyclnex
  89. gpg5ngric
  90. lgricngricex
  91. gpg5edgnedg
  92. grlimedgnedg