W_6

(1, 5)-Jahangir graph | (5, 1)-cone graph | (6, 1)-polyhedral graph | (6, 2)-self dual graph | 6-graph 142 | 6-Halin graph 1 | hexahedral graph 1 | Johnson solid skeleton 2

vertex count | 6 edge count | 10 connected component count | 1

apex | asymmetric | Beineke | biconnected | bridgeless | chromatically nonunique | class 1 | claw-free | cone | connected | cyclic | determined by resistance | determined by spectrum | dominating unique | fully reconstructible in C^1 | graceful | Halin | Hamilton-connected | Hamiltonian | H-star connected | imperfect | Jahangir | Johnson skeleton | linklessly embeddable | map | Metelsky | noncayley | nonempty | noneulerian | nongeometric | Ore | pancyclic | perfect matching | planar | polyhedral | projective planar | quadratically embeddable | rigid | self-dual | simple | switchable | traceable | unigraphic | uniquely embeddable | wheel

pentagon and singleton

6-wheel graph

(not a named graph)

vertex degrees | 3 (5 vertices) | 5 (1 vertex)

radius | 1 diameter | 2 girth | 3 vertex connectivity | 3 edge connectivity | 3

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

x^5 y^5 + 10 x^5 y^4 + 45 x^5 y^3 + 115 x^5 y^2 + 170 x^5 y + 121 x^5 + 5 x^4 y^3 + 40 x^4 y^2 + 126 x^4 y + 170 x^4 + 5 x^3 y^2 + 40 x^3 y + 115 x^3 + 5 x^2 y + 45 x^2 + 10 x + 1

x^5 + 5 x^4 + 5 x^3 y + 10 x^3 + 5 x^2 y^2 + 15 x^2 y + 10 x^2 + 5 x y^3 + 15 x y^2 + 16 x y + 4 x + y^5 + 5 y^4 + 10 y^3 + 10 y^2 + 4 y

chromatic number | 4 edge chromatic number | 5

(1/2 (-1 - sqrt(5)))^2 (1 - sqrt(6))^1 (1/2 (-1 + sqrt(5)))^2 (1 + sqrt(6))^1

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

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

Hosoya index | 36 Kirchhoff index | 8.636 stability index | 26 Wiener index | 20