1-Menger sponge graph | 2-Menger sponge graph | 3-Menger sponge graph

20-edge transitive graph 3

| vertex count | edge count | connected component count 1-Menger sponge graph | 20 | 24 | 1 2-Menger sponge graph | 400 | 672 | 1 3-Menger sponge graph | 8000 | 14976 | 1

asymmetric | bicolorable | biconnected | bipartite | bridgeless | class 1 | connected | cyclic | Menger sponge | noncayley | nonempty | noneulerian | nonhamiltonian | no perfect matching | perfect | simple | triangle-free | uniquely colorable | unit-distance | untraceable | weakly perfect

| complement graph name 1-Menger sponge graph | (not a named graph) 2-Menger sponge graph | (not a named graph) 3-Menger sponge graph | (not a named graph)

| line graph name 1-Menger sponge graph | truncated cubical graph 2-Menger sponge graph | (not a named graph) 3-Menger sponge graph | (not a named graph)

| 1-Menger sponge graph | 2-Menger sponge graph | 3-Menger sponge graph vertex degrees | 2 (12 vertices) | 3 (8 vertices) | 2 (72 vertices) | 3 (152 vertices) | 4 (144 vertices) | 5 (24 vertices) | 6 (8 vertices) | 2 (744 vertices) | 3 (2744 vertices) | 4 (2784 vertices) | 5 (1272 vertices) | 6 (456 vertices)

| radius | diameter | girth 1-Menger sponge graph | 6 | 6 | 8 2-Menger sponge graph | 16 | 24 | 4 3-Menger sponge graph | 49 | 78 | 4 | vertex connectivity | edge connectivity 1-Menger sponge graph | 2 | 2 2-Menger sponge graph | 2 | 2 3-Menger sponge graph | 2 | 2

| 1-Menger sponge graph | 2-Menger sponge graph characteristic polynomial | (x - 2)^3 x^6 (x + 2)^3 (x^2 - 6) (x^2 - 2)^3 | x^30 (x^2 - x - 1) (x^2 + x - 1) (x^4 - 5 x^2 + 3) (x^12 - 33 x^10 + 392 x^8 - 2113 x^6 + 5444 x^4 - 6309 x^2 + 2563) (x^12 - 27 x^10 + 242 x^8 - 855 x^6 + 1158 x^4 - 495 x^2 + 9) (x^12 - 21 x^10 + 153 x^8 - 474 x^6 + 632 x^4 - 342 x^2 + 54)^2 (x^16 - 29 x^14 + 323 x^12 - 1778 x^10 + 5230 x^8 - 8386 x^6 + 7072 x^4 - 2738 x^2 + 312)^2 (x^18 - 26 x^16 + 259 x^14 - 1282 x^12 + 3435 x^10 - 5100 x^8 + 4160 x^6 - 1760 x^4 + 330 x^2 - 18)^3 (x^20 - 32 x^18 + 413 x^16 - 2808 x^14 + 11029 x^12 - 25842 x^10 + 36052 x^8 - 28964 x^6 + 12406 x^4 - 2448 x^2 + 172)^3 (x^28 - 56 x^26 + 1342 x^24 - 18136 x^22 + 153463 x^20 - 854718 x^18 + 3210506 x^16 - 8207370 x^14 + 14247443 x^12 - 16572106 x^10 + 12559510 x^8 - 5892844 x^6 + 1560026 x^4 - 193560 x^2 + 6540)^3 (x^28 - 54 x^26 + 1244 x^24 - 16092 x^22 + 129547 x^20 - 680484 x^18 + 2381042 x^16 - 5572558 x^14 + 8644353 x^12 - 8686018 x^10 + 5420778 x^8 - 1953394 x^6 + 358154 x^4 - 27186 x^2 + 440)^3 rank polynomial | x^19 y^5 + 24 x^19 y^4 + 264 x^19 y^3 + 1696 x^19 y^2 + 6528 x^19 y + 12288 x^19 + 12 x^18 y^4 + 328 x^18 y^3 + 3936 x^18 y^2 + 25728 x^18 y + 78080 x^18 + 162 x^17 y^3 + 4440 x^17 y^2 + 53248 x^17 y + 268032 x^17 + 48 x^16 y^3 + 3260 x^16 y^2 + 76416 x^16 y + 651456 x^16 + 8 x^15 y^3 + 1656 x^15 y^2 + 83448 x^15 y + 1235584 x^15 + 567 x^14 y^2 + 71800 x^14 y + 1912176 x^14 + 120 x^13 y^2 + 49068 x^13 y + 2469744 x^13 + 12 x^12 y^2 + 26400 x^12 y + 2693220 x^12 + 10936 x^11 y + 2492784 x^11 + 3360 x^10 y + 1960536 x^10 + 720 x^9 y + 1307408 x^9 + 96 x^8 y + 735465 x^8 + 6 x^7 y + 346104 x^7 + 134596 x^6 + 42504 x^5 + 10626 x^4 + 2024 x^3 + 276 x^2 + 24 x + 1 | Tutte polynomial | x^19 + 5 x^18 + 15 x^17 + 35 x^16 + 70 x^15 + 126 x^14 + 210 x^13 + 6 x^12 y + 324 x^12 + 24 x^11 y + 465 x^11 + 60 x^10 y + 625 x^10 + 120 x^9 y + 791 x^9 + 226 x^8 y + 929 x^8 + 12 x^7 y^2 + 376 x^7 y + 996 x^7 + 36 x^6 y^2 + 556 x^6 y + 952 x^6 + 99 x^5 y^2 + 698 x^5 y + 787 x^5 + 8 x^4 y^3 + 177 x^4 y^2 + 740 x^4 y + 531 x^4 + 16 x^3 y^3 + 278 x^3 y^2 + 604 x^3 y + 262 x^3 + 66 x^2 y^3 + 276 x^2 y^2 + 322 x^2 y + 80 x^2 + 12 x y^4 + 68 x y^3 + 135 x y^2 + 94 x y + 11 x + y^5 + 7 y^4 + 20 y^3 + 25 y^2 + 11 y |

| chromatic number | edge chromatic number 1-Menger sponge graph | 2 | 3 2-Menger sponge graph | 2 | 6 3-Menger sponge graph | 2 | 6

(-sqrt(6))^1 (-2)^3 (-sqrt(2))^3 0^6 sqrt(2)^3 2^3 sqrt(6)^1

| Hosoya index | Kirchhoff index 1-Menger sponge graph | 26441 | 285.7 2-Menger sponge graph | | 124401 | stability index | Wiener index 1-Menger sponge graph | 23625 | 612 2-Menger sponge graph | 3.011×10^98 | 794976 3-Menger sponge graph | ~ | 954.4 million