12-arc transitive graph 7 | 12-edge transitive graph 11 | 12-quintic graph 6753 | 12-vertex transitive graph 31 | (5, 1)-nonbipartite (0, 2)-graph

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

antipodal | apex | arc-transitive | biconnected | bridgeless | Cayley graphs | class 1 | claw-free | completely regular | connected | cyclic | determined by spectrum | distance-regular | distance-transitive | edge-transitive | graceful | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | imperfect | LCF | local | nonempty | noneulerian | pancyclic | perfect matching | planar | Platonic | polyhedral | projective planar | quintic | regular | simple | symmetric | Taylor | traceable | triangulated | vertex-transitive | weakly regular | zero-two

12-vertex transitive graph 40

dodecahedral graph

line graph of the icosahedral graph

vertex degrees | 5 (12 vertices)

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

(x - 5) (x + 1)^5 (x^2 - 5)^3

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 + ... + 7782 x^4 y + 26835 x^4 + 30 x^3 y^2 + 570 x^3 y + 4040 x^3 + 20 x^2 y + 435 x^2 + 30 x + 1 (93 terms)

x^11 + 19 x^10 + 20 x^9 y + 170 x^9 + 30 x^8 y^2 + 330 x^8 y + 950 x^8 + 60 x^7 y^3 + 610 x^7 y^2 + 2542 x^7 y + 3693 x^7 + ... + 56852 y^10 + 91740 y^9 + 132920 y^8 + 170690 y^7 + 189934 y^6 + 176968 y^5 + 131380 y^4 + 72110 y^3 + 25714 y^2 + 4412 y (92 terms)

chromatic number | 4 edge chromatic number | 5

(-sqrt(5))^3 (-1)^5 sqrt(5)^3 5^1

Hosoya index | 5888 Kirchhoff index | 28 stability index | 8166 Wiener index | 108