first Royle graph | second Royle graph

8-graph 11218

8-graph 11302

| vertex count | edge count | connected component count first Royle graph | 8 | 17 | 1 second Royle graph | 8 | 18 | 1

apex | asymmetric | biconnected | biplanar | bridgeless | chromatically unique | class 1 | connected | cyclic | determined by resistance | determined by spectrum | doublecross | Hamilton-connected | Hamiltonian | H-star connected | noncayley | nonempty | nonplanar | Ore | pancyclic | perfect matching | simple | toroidal | traceable | uniquely colorable | weakly perfect

| complement graph name first Royle graph | 8-graph 7107 second Royle graph | (not a named graph)

| line graph name first Royle graph | (not a named graph) second Royle graph | (not a named graph)

| first Royle graph | second Royle graph vertex degrees | 4 (7 vertices) | 6 (1 vertex) | 4 (5 vertices) | 5 (2 vertices) | 6 (1 vertex)

| radius | diameter | girth first Royle graph | 2 | 2 | 3 second Royle graph | 2 | 2 | 3 | vertex connectivity | edge connectivity first Royle graph | 4 | 4 second Royle graph | 4 | 4

| first Royle graph | second Royle graph characteristic polynomial | (x - 1) (x + 1) (x^2 + 2 x - 1) (x^4 - 2 x^3 - 11 x^2 + 2 x + 8) | (x - 1) (x + 1) (x^6 - 17 x^4 - 22 x^3 + 15 x^2 + 10 x - 1) rank polynomial | x^7 y^10 + 17 x^7 y^9 + 136 x^7 y^8 + 680 x^7 y^7 + 2373 x^7 y^6 + 6097 x^7 y^5 + 11816 x^7 y^4 + 17314 x^7 y^3 + 18734 x^7 y^2 + 13880 x^7 y + 5520 x^7 + 7 x^6 y^7 + 91 x^6 y^6 + 560 x^6 y^5 + 2123 x^6 y^4 + 5450 x^6 y^3 + 9751 x^6 y^2 + 11669 x^6 y + 7467 x^6 + 11 x^5 y^5 + 126 x^5 y^4 + 677 x^5 y^3 + 2225 x^5 y^2 + 4651 x^5 y + 5091 x^5 + 2 x^4 y^4 + 34 x^4 y^3 + 258 x^4 y^2 + 1085 x^4 y + 2234 x^4 + 12 x^3 y^2 + 146 x^3 y + 671 x^3 + 9 x^2 y + 136 x^2 + 17 x + 1 | x^7 y^11 + 18 x^7 y^10 + 153 x^7 y^9 + 816 x^7 y^8 + 3055 x^7 y^7 + 8496 x^7 y^6 + 18078 x^7 y^5 + 29787 x^7 y^4 + 37842 x^7 y^3 + 36058 x^7 y^2 + 23827 x^7 y + 8535 x^7 + 5 x^6 y^8 + 72 x^6 y^7 + 486 x^6 y^6 + 2033 x^6 y^5 + 5859 x^6 y^4 + 12191 x^6 y^3 + 18450 x^6 y^2 + 19239 x^6 y + 10940 x^6 + 4 x^5 y^6 + 57 x^5 y^5 + 371 x^5 y^4 + 1476 x^5 y^3 + 3985 x^5 y^2 + 7206 x^5 y + 6995 x^5 + 5 x^4 y^4 + 65 x^4 y^3 + 418 x^4 y^2 + 1556 x^4 y + 2867 x^4 + 17 x^3 y^2 + 193 x^3 y + 805 x^3 + 11 x^2 y + 153 x^2 + 18 x + 1 Tutte polynomial | x^7 + 10 x^6 + 9 x^5 y + 46 x^5 + 12 x^4 y^2 + 77 x^4 y + 122 x^4 + 2 x^3 y^4 + 26 x^3 y^3 + 120 x^3 y^2 + 265 x^3 y + 192 x^3 + 11 x^2 y^5 + 65 x^2 y^4 + 205 x^2 y^3 + 408 x^2 y^2 + 436 x^2 y + 164 x^2 + 7 x y^7 + 42 x y^6 + 139 x y^5 + 307 x y^4 + 495 x y^3 + 533 x y^2 + 308 x y + 57 x + y^10 + 7 y^9 + 28 y^8 + 77 y^7 + 161 y^6 + 263 y^5 + 340 y^4 + 326 y^3 + 201 y^2 + 57 y | x^7 + 11 x^6 + 11 x^5 y + 55 x^5 + 17 x^4 y^2 + 104 x^4 y + 154 x^4 + 5 x^3 y^4 + 45 x^3 y^3 + 185 x^3 y^2 + 369 x^3 y + 248 x^3 + 4 x^2 y^6 + 33 x^2 y^5 + 131 x^2 y^4 + 347 x^2 y^3 + 616 x^2 y^2 + 600 x^2 y + 212 x^2 + 5 x y^8 + 32 x y^7 + 114 x y^6 + 283 x y^5 + 537 x y^4 + 776 x y^3 + 764 x y^2 + 411 x y + 73 x + y^11 + 7 y^10 + 28 y^9 + 79 y^8 + 173 y^7 + 307 y^6 + 449 y^5 + 531 y^4 + 472 y^3 + 272 y^2 + 73 y

| chromatic number | edge chromatic number first Royle graph | 3 | 6 second Royle graph | 3 | 6

(-1 - sqrt(2))^1 (root of 8 + 2 x - 11 x^2 - 2 x^3 + x^4 near x = -2.38061)^1 (-1)^1 (root of 8 + 2 x - 11 x^2 - 2 x^3 + x^4 near x = -0.857382)^1 (-1 + sqrt(2))^1 (root of 8 + 2 x - 11 x^2 - 2 x^3 + x^4 near x = 0.904451)^1 1^1 (root of 8 + 2 x - 11 x^2 - 2 x^3 + x^4 near x = 4.33354)^1

(root of -1 + 10 x + 15 x^2 - 22 x^3 - 17 x^4 + x^6 near x = -2.72071)^1 (root of -1 + 10 x + 15 x^2 - 22 x^3 - 17 x^4 + x^6 near x = -2.17489)^1 (-1)^1 (root of -1 + 10 x + 15 x^2 - 22 x^3 - 17 x^4 + x^6 near x = -0.538833)^1 (root of -1 + 10 x + 15 x^2 - 22 x^3 - 17 x^4 + x^6 near x = 0.0896411)^1 (root of -1 + 10 x + 15 x^2 - 22 x^3 - 17 x^4 + x^6 near x = 0.763756)^1 1^1 (root of -1 + 10 x + 15 x^2 - 22 x^3 - 17 x^4 + x^6 near x = 4.58104)^1

| adjacency matrix first Royle graph | (0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0) second Royle graph | (0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0) | incidence matrix first Royle graph | (1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1) second Royle graph | (1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1)

| Hosoya index | Kirchhoff index first Royle graph | 214 | 12.81 second Royle graph | 242 | 11.99 | stability index | Wiener index first Royle graph | 96 | 39 second Royle graph | 68 | 38