6-graph 131

vertex count | 6 edge count | 11 connected component count | 1

apex | asymmetric | Beineke | biconnected | bridgeless | chordal | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | distance-hereditary | dominating nonunique | graceful | Hamiltonian | king | linklessly embeddable | map | Metelsky | Meyniel | noncayley | nonempty | noneulerian | nongeometric | Ore | pancyclic | perfect | perfect matching | planar | projective planar | Ptolemaic | quadratically embeddable | rigid | simple | strongly perfect | switchable | traceable | unigraphic | uniquely embeddable | weakly perfect

square and two singletons

(not a named graph)

vertex degrees | 3 (4 vertices) | 5 (2 vertices)

radius | 1 diameter | 2 girth | 3 vertex connectivity | 2 edge connectivity | 3

(x - 1) (x + 1)^3 (x^2 - 2 x - 7)

x^5 y^6 + 11 x^5 y^5 + 55 x^5 y^4 + 161 x^5 y^3 + 296 x^5 y^2 + 336 x^5 y + 192 x^5 + 4 x^4 y^4 + 34 x^4 y^3 + 124 x^4 y^2 + 254 x^4 y + 256 x^4 + 2 x^3 y^3 + 16 x^3 y^2 + 74 x^3 y + 157 x^3 + 8 x^2 y + 55 x^2 + 11 x + 1

x^5 + 6 x^4 + 8 x^3 y + 13 x^3 + 2 x^2 y^3 + 10 x^2 y^2 + 24 x^2 y + 12 x^2 + 4 x y^4 + 14 x y^3 + 26 x y^2 + 20 x y + 4 x + y^6 + 5 y^5 + 11 y^4 + 15 y^3 + 12 y^2 + 4 y

chromatic number | 4 edge chromatic number | 5

(1 - 2 sqrt(2))^1 (-1)^3 1^1 (1 + 2 sqrt(2))^1

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

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

Hosoya index | 40 Kirchhoff index | 8 stability index | 22 Wiener index | 19