(K_2 square K_6)^_

12-arc transitive graph 8 | 12-edge transitive graph 10 | 12-quintic graph 7848 | 12-vertex transitive graph 25 | (2, 6)-rook complement graph | 47-Haar graph | 55-Haar graph | 59-Haar graph | (6, 1)-bipartite Kneser graph | 61-Haar graph | 62-Haar graph

vertex count | 12 edge count | 30 connected component count | 1

antipodal | arc-transitive | bicolorable | biconnected | bipartite | bipartite Kneser | biplanar | bridgeless | Cayley graphs | class 1 | conformally rigid | connected | crown | cyclic | distance-regular | distance-transitive | dominating nonunique | edge-transitive | fully reconstructible in C^1 | geometric | Haar | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | H-star connected | integral | intrinsically linked | LCF | local | Meyniel | multigraphic | nonempty | noneulerian | nonplanar | not uniquely embeddable | perfect | perfect matching | pretzel | quintic | regular | rigid | rook complement | simple | switchable | symmetric | Taylor | traceable | triangle-free | uniquely colorable | vertex-transitive | weakly perfect | weakly regular

(2, 6)-rook graph

(6, 2)-arrangement graph

vertex degrees | 5 (12 vertices)

radius | 3 diameter | 3 girth | 4 vertex connectivity | 5 edge connectivity | 5

(x - 5) (x - 1)^5 (x + 1)^5 (x + 5)

x^11 y^19 + 30 x^11 y^18 + 435 x^11 y^17 + 4060 x^11 y^16 + 27405 x^11 y^15 + 142494 x^11 y^14 + 593475 x^11 y^13 + 2032200 x^11 y^12 + 5825295 x^11 y^11 + ... + 140166 x^5 + 120 x^4 y^2 + 2340 x^4 y + 27315 x^4 + 90 x^3 y + 4060 x^3 + 435 x^2 + 30 x + 1 (86 terms)

x^11 + 19 x^10 + 190 x^9 + 90 x^8 y + 1240 x^8 + 120 x^7 y^2 + 1380 x^7 y + 5725 x^7 + 20 x^6 y^4 + 310 x^6 y^3 + ... + 57068 y^10 + 93016 y^9 + 138116 y^8 + 186446 y^7 + 226553 y^6 + 242177 y^5 + 217906 y^4 + 152436 y^3 + 71701 y^2 + 16369 y (85 terms)

chromatic number | 2 edge chromatic number | 5

(-5)^1 (-1)^5 1^5 5^1

Hosoya index | 6600 Kirchhoff index | 26.2 stability index | 832 Wiener index | 108