K_5

(1, 5)-Hamming graph | (1, 5)-lattice graph | (1, 5)-queen graph | (1, 5)-rook graph | (4, 5)-Harary graph | 4-tree (5, 1) | (5, 1)-arrangement graph | (5, 1)-Johnson graph | (5, 1)-Kneser graph | (5, 1)-KP graph | ...

vertex count | 5 edge count | 10 connected component count | 1

apex | arc-transitive | arrangement | biconnected | biplanar | block | bridgeless | cage | Cayley graphs | chordal | chromatically unique | circulant | class 2 | claw-free | complete | complete k-partite | conformally rigid | connected | critical nonplanar | 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 | Johnson | Kneser | KP | k-tree | Kuratowski | LCF | line graphs | linklessly embeddable | local | Meyniel | Moore | nonempty | nonplanar | no perfect matching | not uniquely embeddable | Ore | pancyclic | perfect | projective planar | Ptolemaic | quadratically embeddable | quartic | queen | regular | rigid | rook | simple | singlecross | split | strongly perfect | strongly regular | symmetric | toroidal | traceable | Turán | ungraceful | unigraphic | uniquely colorable | unswitchable | vertex-transitive | weakly perfect | well covered

5-empty graph

5-triangular graph

vertex degrees | 4 (5 vertices)

radius | 1 diameter | 1 girth | 3 vertex connectivity | 4 edge connectivity | 4

(x - 4) (x + 1)^4

x^4 y^6 + 10 x^4 y^5 + 45 x^4 y^4 + 120 x^4 y^3 + 205 x^4 y^2 + 222 x^4 y + 125 x^4 + 5 x^3 y^3 + 30 x^3 y^2 + 85 x^3 y + 110 x^3 + 10 x^2 y + 45 x^2 + 10 x + 1

x^4 + 6 x^3 + 10 x^2 y + 11 x^2 + 5 x y^3 + 15 x y^2 + 20 x y + 6 x + y^6 + 4 y^5 + 10 y^4 + 15 y^3 + 15 y^2 + 6 y

chromatic number | 5 edge chromatic number | 5

(-1)^4 4^1

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

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

Hosoya index | 26 Kirchhoff index | 4 stability index | 24 Wiener index | 10