6-graph 54 | 6-matchstick graph 19

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

almost controllable | apex | asymmetric | bicolorable | bipartite | bridged | cactus | chordless | chromatically nonunique | class 1 | connected | cyclic | determined by resistance | determined by spectrum | distance-hereditary | dominating unique | flexible | graceful | linklessly embeddable | map | matchstick | median | Meyniel | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonhamiltonian | outerplanar | perfect | perfect matching | planar | projective planar | pseudoforest | pseudotree | quadratically embeddable | simple | switchable | tadpole | traceable | triangle-free | unicyclic | uniquely colorable | uniquely embeddable | unit-distance | weakly perfect

6-graph 128

antenna graph

vertex degrees | 1 (1 vertex) | 2 (4 vertices) | 3 (1 vertex)

radius | 2 diameter | 4 girth | 4 vertex connectivity | 1 edge connectivity | 1

x^2 (x^4 - 6 x^2 + 6)

(x + 1)^2 (x^3 y + 4 x^3 + 6 x^2 + 4 x + 1)

x^2 (x^3 + x^2 + x + y)

chromatic number | 2 edge chromatic number | 3

(-sqrt(3 + sqrt(3)))^1 (-sqrt(3 - sqrt(3)))^1 0^2 sqrt(3 - sqrt(3))^1 sqrt(3 + sqrt(3))^1

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

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

Hosoya index | 17 Kirchhoff index | 23 stability index | 13 Wiener index | 29