7-graph 836
vertex count | 7 edge count | 12 connected component count | 1
apex | asymmetric | biconnected | biplanar | bridgeless | chromatically nonunique | class 1 | connected | critical nonplanar | cyclic | determined by resistance | determined by spectrum | dominating nonunique | Eulerian | graceful | Hamiltonian | imperfect | linklessly embeddable | multigraphic | noncayley | nonempty | nongeometric | nonplanar | no perfect matching | not uniquely embeddable | nut | pancyclic | projective planar | rigid | simple | singlecross | switchable | toroidal | traceable | weakly perfect
9-matchstick graph 45
(not a named graph)
vertex degrees | 2 (2 vertices) | 4 (5 vertices)
radius | 2 diameter | 2 girth | 3 vertex connectivity | 2 edge connectivity | 2
x (x + 1) (x^2 + x - 1) (x^3 - 2 x^2 - 8 x + 7)
x^6 y^6 + 12 x^6 y^5 + 64 x^6 y^4 + 200 x^6 y^3 + 396 x^6 y^2 + 492 x^6 y + 315 x^6 + 2 x^5 y^5 + 20 x^5 y^4 + 98 x^5 y^3 + 286 x^5 y^2 + 535 x^5 y + 545 <<1>> + ... + 14 x^4 y^3 + 73 x^4 y^2 + 239 x^4 y + 441 x^4 + x^3 y^3 + 8 x^3 y^2 + 54 x^3 y + 215 x^3 + 5 x^2 y + 66 x^2 + 12 x + 1 (26 terms)
x^6 + 6 x^5 + 5 x^4 y + 16 x^4 + x^3 y^3 + 5 x^3 y^2 + 21 x^3 y + 24 x^3 + x^2 y^4 + 7 x^2 y^3 + 22 x^2 y^2 + 38 x^2 y + 19 x^2 + 2 x y^5 + 8 x y^4 + 21 x y^3 + 33 x y^2 + 28 x y + 6 x + y^6 + 4 y^5 + 10 y^4 + 15 y^3 + 15 y^2 + 6 y
chromatic number | 4 edge chromatic number | 4
(root of 7 - 8 x - 2 x^2 + x^3 near x = -2.44437)^1 (1/2 (-1 - sqrt(5)))^1 (-1)^1 0^1 (1/2 (-1 + sqrt(5)))^1 (root of 7 - 8 x - 2 x^2 + x^3 near x = 0.78191)^1 (root of 7 - 8 x - 2 x^2 + x^3 near x = 3.66246)^1
(0 | 0 | 0 | 1 | 1 | 1 | 1 0 | 0 | 0 | 1 | 0 | 1 | 0 0 | 0 | 0 | 0 | 1 | 1 | 0 1 | 1 | 0 | 0 | 1 | 0 | 1 1 | 0 | 1 | 1 | 0 | 0 | 1 1 | 1 | 1 | 0 | 0 | 0 | 1 1 | 0 | 0 | 1 | 1 | 1 | 0)
(1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1)
Hosoya index | 66 Kirchhoff index | 13.13 stability index | 18 Wiener index | 30