10-graph 12005168
K_10
vertex count | 10 edge count | 45 connected component count | 1
arc-transitive | biconnected | block | bridgeless | cage | Cayley graphs | chordal | chromatically unique | circulant | class 1 | claw-free | complete | complete k-partite | conformally rigid | connected | cyclic | determined by resistance | determined by spectrum | distance-hereditary | distance-regular | distance-transitive | dominating unique | edge-transitive | fully reconstructible in C^1 | geodetic | geometric | Hamilton-connected | Hamilton-decomposable | Hamiltonian | Hamming | Harary | H-star connected | integral | intrinsically linked | Johnson | Kneser | KP | k-tree | LCF | line graphs | local | Meyniel | Moore | nonempty | noneulerian | nonplanar | not uniquely embeddable | Ore | pancyclic | perfect | perfect matching | Ptolemaic | quadratically embeddable | queen | regular | rigid | rook | simple | split | strongly perfect | strongly regular | symmetric | traceable | Turán | ungraceful | unigraphic | uniquely colorable | unswitchable | vertex-transitive | weakly perfect | well covered
10-empty graph
10-triangular graph
vertex degrees | 9 (10 vertices)
radius | 1 diameter | 1 girth | 3 vertex connectivity | 9 edge connectivity | 9
(x - 9) (x + 1)^9
x^9 y^36 + 45 x^9 y^35 + 990 x^9 y^34 + 14190 x^9 y^33 + 148995 x^9 y^32 + 1221759 x^9 y^31 + 8145060 x^9 y^30 + 45379620 x^9 y^29 + ... + 26100000 x^7 + 6258000 x^6 + 1092105 x^5 + 143325 x^4 + 14070 x^3 + 990 x^2 + 45 x + 1 (130 terms)
y^36 + 9 y^35 + 45 y^34 + 165 y^33 + 495 y^32 + 1287 y^31 + 3003 y^30 + 6435 y^29 + 10 x y^28 + 12860 y^28 + 80 x y^27 + 24220 y^27 + ... + 314928 x y + 40320 y + x^9 + 36 x^8 + 546 x^7 + 4536 x^6 + 22449 x^5 + 67284 x^4 + 118124 x^3 + 109584 x^2 + 40320 x (129 terms)
chromatic number | 10 edge chromatic number | 9
(-1)^9 9^1
Hosoya index | 9496 Kirchhoff index | 9 stability index | 2050 Wiener index | 45