K_7

(1, 7)-Hamming graph | (1, 7)-lattice graph | (1, 7)-queen graph | (1, 7)-rook graph | (6, 7)-Harary graph | 6-tree (7, 1) | (7, 1)-Johnson graph | (7, 1)-Kneser graph | (7, 1)-KP graph | (7, 1)-torus triangulation graph | ...

vertex count | 7 edge count | 21 connected component count | 1

arc-transitive | biconnected | biplanar | block | bridgeless | cage | Cayley graphs | chordal | chromatically unique | circulant | class 2 | 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 | Eulerian | 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 | nonplanar | no perfect matching | not uniquely embeddable | Ore | pancyclic | perfect | Ptolemaic | quadratically embeddable | queen | regular | rigid | rook | sextic | simple | split | strongly perfect | strongly regular | symmetric | toroidal | torus triangulation | traceable | Turán | ungraceful | unigraphic | uniquely colorable | unswitchable | vertex-transitive | weakly perfect | well covered

7-empty graph

7-triangular graph

vertex degrees | 6 (7 vertices)

radius | 1 diameter | 1 girth | 3 vertex connectivity | 6 edge connectivity | 6

(x - 6) (x + 1)^6

x^6 y^15 + 21 x^6 y^14 + 210 x^6 y^13 + 1330 x^6 y^12 + 5985 x^6 y^11 + 20349 x^6 y^10 + 54257 x^6 y^9 + 116175 x^6 y^8 + 202755 x^6 y^7 + 290745 x^6 y^6 + ... + 6762 x^4 y + 5250 x^4 + 35 x^3 y^3 + 210 x^3 y^2 + 735 x^3 y + 1295 x^3 + 35 x^2 y + 210 x^2 + 21 x + 1 (42 terms)

x^6 + 15 x^5 + 35 x^4 y + 85 x^4 + 35 x^3 y^3 + 105 x^3 y^2 + 280 x^3 y + 225 x^3 + 21 x^2 y^6 + 84 x^2 y^5 + 210 x^2 y^4 + 420 x^2 y^3 + ... + 56 y^12 + 126 y^11 + 245 y^10 + 420 y^9 + 645 y^8 + 895 y^7 + 1120 y^6 + 1260 y^5 + 1225 y^4 + 945 y^3 + 490 y^2 + 120 y (41 terms)

chromatic number | 7 edge chromatic number | 7

(-1)^6 6^1

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

Hosoya index | 232 Kirchhoff index | 6 stability index | 160 Wiener index | 21