2-Plummer-Toft graph

(7, 1)-self dual graph | (7, 24)-polyhedral graph | 7-graph 969 | heptahedral graph 24 | heptahedral graph 24 dual | Johnson solid skeleton 7 | self-dual graph 1

vertex count | 7 edge count | 12 connected component count | 1

apex | asymmetric | biconnected | bridgeless | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | dominating nonunique | fully reconstructible in C^1 | graceful | Hamilton-connected | Hamiltonian | H-star connected | Johnson skeleton | line graphs | linklessly embeddable | map | multigraphic | noncayley | nonempty | noneulerian | nongeometric | no perfect matching | pancyclic | perfect | planar | Plummer-Toft | polyhedral | projective planar | quadratically embeddable | rigid | self-dual | simple | switchable | traceable | uniquely embeddable | weakly perfect | well covered

3-gear graph

2-Plummer-Toft graph

(not a named graph)

vertex degrees | 3 (4 vertices) | 4 (3 vertices)

radius | 2 diameter | 2 girth | 3 vertex connectivity | 3 edge connectivity | 3

x^2 (x + 2)^2 (x^3 - 4 x^2 + 6)

x^6 y^6 + 12 x^6 y^5 + 66 x^6 y^4 + 215 x^6 y^3 + 444 x^6 y^2 + 567 x^6 y + 361 x^6 + 5 x^5 y^4 + 51 x^5 y^3 + 219 x^5 y^2 + 513 x^5 y + 567 x^5 + 6 x^4 y^3 + 49 x^4 y^2 + 219 x^4 y + 444 x^4 + x^3 y^3 + 6 x^3 y^2 + 51 x^3 y + 215 x^3 + 5 x^2 y + 66 x^2 + 12 x + 1

x^6 + 6 x^5 + 5 x^4 y + 16 x^4 + x^3 y^3 + 3 x^3 y^2 + 22 x^3 y + 25 x^3 + 3 x^2 y^3 + 22 x^2 y^2 + 43 x^2 y + 22 x^2 + 5 x y^4 + 22 x y^3 + 43 x y^2 + 36 x y + 8 x + y^6 + 6 y^5 + 16 y^4 + 25 y^3 + 22 y^2 + 8 y

chromatic number | 4 edge chromatic number | 4

(-2)^2 (root of 6 - 4 x^2 + x^3 near x = -1.08613)^1 0^2 (root of 6 - 4 x^2 + x^3 near x = 1.57199)^1 (root of 6 - 4 x^2 + x^3 near x = 3.51414)^1

(0 | 1 | 1 | 1 | 0 | 0 | 1 1 | 0 | 1 | 0 | 1 | 0 | 1 1 | 1 | 0 | 0 | 0 | 1 | 1 1 | 0 | 0 | 0 | 1 | 1 | 0 0 | 1 | 0 | 1 | 0 | 1 | 0 0 | 0 | 1 | 1 | 1 | 0 | 0 1 | 1 | 1 | 0 | 0 | 0 | 0)

(1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0)

Hosoya index | 71 Kirchhoff index | 12.63 stability index | 34 Wiener index | 30