K_6

(1, 6)-Hamming graph | (1, 6)-lattice graph | (1, 6)-queen graph | (1, 6)-rook graph | (5, 6)-Harary graph | (6, 1)-arrangement graph | (6, 1)-Johnson graph | (6, 1)-Kneser graph | (6, 6)-Turán graph | 6-arc transitive graph 4 | ...

vertex count | 6 edge count | 15 connected component count | 1

arc-transitive | arrangement | biconnected | biplanar | bridgeless | cage | Cayley graphs | chordal | chromatically unique | circulant | class 1 | claw-free | complete | complete k-partite | connected | cyclic | determined by resistance | determined by spectrum | distance-regular | distance-transitive | edge-transitive | geodetic | Hamilton-connected | Hamilton-decomposable | Hamiltonian | Hamming | Harary | H-star connected | integral | Johnson | Kneser | LCF | line graphs | local | Moore | nonempty | noneulerian | nonplanar | Ore | pancyclic | perfect | perfect matching | projective planar | queen | quintic | regular | rook | simple | split | strongly perfect | strongly regular | symmetric | toroidal | traceable | Turán | ungraceful | uniquely colorable | vertex-transitive | weakly perfect | well covered

6-empty graph

6-triangular graph

vertex degrees | 5 (6 vertices)

radius | 1 diameter | 1 girth | 3 vertex connectivity | 5 edge connectivity | 5

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

x^5 y^10 + 15 x^5 y^9 + 105 x^5 y^8 + 455 x^5 y^7 + 1365 x^5 y^6 + 2997 x^5 y^5 + 4945 x^5 y^4 + 6165 x^5 y^3 + 5700 x^5 y^2 + 3660 x^5 y + 1296 x^5 + ... + 1330 x^4 y^2 + 1617 x^4 y + 1080 x^4 + 15 x^3 y^3 + 90 x^3 y^2 + 285 x^3 y + 435 x^3 + 20 x^2 y + 105 x^2 + 15 x + 1 (26 terms)

x^5 + 10 x^4 + 20 x^3 y + 35 x^3 + 15 x^2 y^3 + 45 x^2 y^2 + 90 x^2 y + 50 x^2 + 6 x y^6 + 24 x y^5 + 60 x y^4 + 105 x y^3 + 145 x y^2 + 106 x y + 24 x + y^10 + 5 y^9 + 15 y^8 + 35 y^7 + 64 y^6 + 96 y^5 + 120 y^4 + 120 y^3 + 80 y^2 + 24 y

chromatic number | 6 edge chromatic number | 5

(-1)^5 5^1

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

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

Hosoya index | 76 Kirchhoff index | 5 stability index | 66 Wiener index | 15