8-graph 12315
P^__8
vertex count | 8 edge count | 21 connected component count | 1
asymmetric | biconnected | biplanar | bridgeless | chromatically unique | 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 | intrinsically linked | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonplanar | not uniquely embeddable | Ore | pancyclic | path complement | perfect | perfect matching | rigid | simple | switchable | toroidal | traceable | uniquely colorable | weakly perfect | well covered
8-path graph
(not a named graph)
vertex degrees | 5 (6 vertices) | 6 (2 vertices)
radius | 2 diameter | 2 girth | 3 vertex connectivity | 5 edge connectivity | 5
x (x^3 + 3 x^2 - 3) (x^4 - 3 x^3 - 12 x^2 - x + 4)
x^7 y^14 + 21 x^7 y^13 + 210 x^7 y^12 + 1330 x^7 y^11 + 5985 x^7 y^10 + 20343 x^7 y^9 + 54166 x^7 y^8 + 115530 x^7 y^7 + 199910 x^7 y^6 + 281975 x^7 y^5 + ... + 3951 x^4 y + 5570 x^4 + 5 x^3 y^3 + 60 x^3 y^2 + 415 x^3 y + 1310 x^3 + 20 x^2 y + 210 x^2 + 21 x + 1 (48 terms)
x^7 + 14 x^6 + 20 x^5 y + 85 x^5 + 5 x^4 y^3 + 45 x^4 y^2 + 210 x^4 y + 280 x^4 + 4 x^3 y^5 + 40 x^3 y^4 + 167 x^3 y^3 + 491 x^3 y^2 + 828 x^3 y + ... + 28 y^12 + 84 y^11 + 204 y^10 + 418 y^9 + 742 y^8 + 1156 y^7 + 1585 y^6 + 1888 y^5 + 1881 y^4 + 1449 y^3 + 743 y^2 + 182 y (47 terms)
chromatic number | 4 edge chromatic number | 6
(root of -3 + 3 x^2 + x^3 near x = -2.53209)^1 (root of 4 - x - 12 x^2 - 3 x^3 + x^4 near x = -2.08467)^1 (root of -3 + 3 x^2 + x^3 near x = -1.3473)^1 (root of 4 - x - 12 x^2 - 3 x^3 + x^4 near x = -0.708873)^1 0^1 (root of 4 - x - 12 x^2 - 3 x^3 + x^4 near x = 0.512552)^1 (root of -3 + 3 x^2 + x^3 near x = 0.879385)^1 (root of 4 - x - 12 x^2 - 3 x^3 + x^4 near x = 5.281)^1
(0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0)
Hosoya index | 363 Kirchhoff index | 9.814 stability index | 35 Wiener index | 35