5-graph 31

vertex count | 5 edge count | 7 connected component count | 1

apex | asymmetric | Beineke | biconnected | bridgeless | chromatically unique | class 2 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | distance-hereditary | dominating unique | graceful | Hamiltonian | Laman | linklessly embeddable | map | Metelsky | Meyniel | noncayley | nonempty | noneulerian | nongeometric | no perfect matching | Ore | pancyclic | perfect | planar | projective planar | rigid | simple | strongly perfect | switchable | traceable | unigraphic | uniquely embeddable | weakly perfect | well covered

3-path and 2-path

Johnson solid skeleton 49

vertex degrees | 2 (1 vertex) | 3 (4 vertices)

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

x (x + 1) (x^3 - x^2 - 6 x + 2)

x^4 y^3 + 7 x^4 y^2 + 20 x^4 y + 24 x^4 + x^3 y^2 + 11 x^3 y + 33 x^3 + 2 x^2 y + 21 x^2 + 7 x + 1

x^4 + 3 x^3 + 2 x^2 y + 4 x^2 + x y^2 + 5 x y + 2 x + y^3 + 3 y^2 + 2 y

chromatic number | 3 edge chromatic number | 4

(root of 2 - 6 x - x^2 + x^3 near x = -2.17741)^1 (-1)^1 0^1 (root of 2 - 6 x - x^2 + x^3 near x = 0.321637)^1 (root of 2 - 6 x - x^2 + x^3 near x = 2.85577)^1

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

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

Hosoya index | 16 Kirchhoff index | 6.417 stability index | 4 Wiener index | 13