10-hypohamiltonian Graph 1
GP(5, 2)
vertex count | 10 edge count | 15 connected component count | 1
almost Hamiltonian | arc-transitive | biconnected | biplanar | bridgeless | cage | chromatically unique | class 2 | conformally rigid | connected | cubic | cyclic | determined by resistance | determined by spectrum | distance-regular | distance-transitive | dominating unique | doublecross | edge-transitive | flexible | fully reconstructible in C^1 | generalized Petersen | geodetic | graceful | hypohamiltonian | I graphs | imperfect | integral | intrinsically linked | Kneser | Lindgren-Sousselier | local | maximally nonhamiltonian | Moore | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonhamiltonian | nonplanar | not uniquely embeddable | odd | perfect matching | Petersen family | projective planar | quadratically embeddable | regular | simple | snark | square-free | strongly regular | switchable | symmetric | toroidal | traceable | triangle-free | unit-distance | vertex-transitive | weak snark
5-triangular graph
Petersen line graph
vertex degrees | 3 (10 vertices)
radius | 2 diameter | 2 girth | 5 vertex connectivity | 3 edge connectivity | 3
(x - 3) (x - 1)^5 (x + 2)^4
x^9 y^6 + 15 x^9 y^5 + 105 x^9 y^4 + 445 x^9 y^3 + 1230 x^9 y^2 + 2172 x^9 y + 2000 x^9 + 10 x^8 y^4 + 135 x^8 y^3 + 816 x^8 y^2 + 2765 x^8 y + ... + 30 x^6 y^2 + 630 x^6 y + 4875 x^6 + 130 x^5 y + 2991 x^5 + 12 x^4 y + 1365 x^4 + 455 x^3 + 105 x^2 + 15 x + 1 (27 terms)
x^9 + 6 x^8 + 21 x^7 + 56 x^6 + 12 x^5 y + 114 x^5 + 70 x^4 y + 170 x^4 + 30 x^3 y^2 + 170 x^3 y + 180 x^3 + 15 x^2 y^3 + 105 x^2 y^2 + 240 x^2 y + 120 x^2 + 10 x y^4 + 65 x y^3 + 171 x y^2 + 168 x y + 36 x + y^6 + 9 y^5 + 35 y^4 + 75 y^3 + 84 y^2 + 36 y
chromatic number | 3 edge chromatic number | 4
(-2)^4 1^5 3^1
Hosoya index | 332 Kirchhoff index | 33 stability index | 424 Wiener index | 75