9-graph 274620
P^__9
vertex count | 9 edge count | 28 connected component count | 1
asymmetric | biconnected | biplanar | 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 | intrinsically linked | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonplanar | no perfect matching | not uniquely embeddable | Ore | pancyclic | path complement | perfect | projective planar | rigid | simple | switchable | traceable | uniquely graceful | weakly perfect | well covered
9-path graph
(not a named graph)
vertex degrees | 6 (7 vertices) | 7 (2 vertices)
radius | 2 diameter | 2 girth | 3 vertex connectivity | 6 edge connectivity | 6
(x^2 + x - 1) (x^2 + 3 x + 1) (x^5 - 4 x^4 - 15 x^3 + 4 x^2 + 13 x - 2)
x^8 y^20 + 28 x^8 y^19 + 378 x^8 y^18 + 3276 x^8 y^17 + 20475 x^8 y^16 + 98280 x^8 y^15 + 376733 x^8 y^14 + 1183884 x^8 y^13 + 3106446 x^8 y^12 + 6895700 x^8 y^11 + ... + 19480 x^4 + 15 x^3 y^3 + 150 x^3 y^2 + 995 x^3 y + 3241 x^3 + 35 x^2 y + 378 x^2 + 28 x + 1 (73 terms)
x^8 + 20 x^7 + 35 x^6 y + 175 x^6 + 15 x^5 y^3 + 105 x^5 y^2 + 530 x^5 y + 855 x^5 + x^4 y^6 + 24 x^4 y^5 + 150 x^4 y^4 + 555 x^4 y^3 + ... + 8890 y^11 + 13265 y^10 + 18399 y^9 + 23705 y^8 + 28204 y^7 + 30560 y^6 + 29356 y^5 + 23846 y^4 + 15105 y^3 + 6457 y^2 + 1350 y (72 terms)
chromatic number | 5 edge chromatic number | 7
(1/2 (-3 - sqrt(5)))^1 (root of -2 + 13 x + 4 x^2 - 15 x^3 - 4 x^4 + x^5 near x = -2.24583)^1 (1/2 (-1 - sqrt(5)))^1 (root of -2 + 13 x + 4 x^2 - 15 x^3 - 4 x^4 + x^5 near x = -1.05068)^1 (1/2 (-3 + sqrt(5)))^1 (root of -2 + 13 x + 4 x^2 - 15 x^3 - 4 x^4 + x^5 near x = 0.150957)^1 (1/2 (-1 + sqrt(5)))^1 (root of -2 + 13 x + 4 x^2 - 15 x^3 - 4 x^4 + x^5 near x = 0.898824)^1 (root of -2 + 13 x + 4 x^2 - 15 x^3 - 4 x^4 + x^5 near x = 6.24673)^1
(0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0)
Hosoya index | 1235 Kirchhoff index | 10.67 stability index | 204 Wiener index | 44