S_7

(1, 6)-complete 2-partite graph | (1, 6)-complete bipartite graph | 1-tree (7, 2) | (6, 1)-Cayley tree | (6, 1)-spoke graph | (6, 1)-stacked book graph | 6-matchstick graph 12 | 7-edge-transitive graph 27 | 7-graph 7 | 7-tree 2 | 7-uniquely graceful graph 1

vertex count | 7 edge count | 6 connected component count | 1

acyclic | apex | asymmetric | bicolorable | bipartite | block | bridged | cactus | caterpillar | chordal | chordless | chromatically nonunique | class 1 | complete bipartite | complete k-partite | complete tree | conformally rigid | connected | determined by resistance | distance-hereditary | dominating unique | edge-transitive | flexible | forest | geodetic | graceful | k-tree | linklessly embeddable | lobster | map | matchstick | median | Meyniel | noncayley | nonempty | noneulerian | nongeometric | nonhamiltonian | no perfect matching | not determined by spectrum | outerplanar | perfect | planar | projective planar | pseudoforest | pseudotree | Ptolemaic | quadratically embeddable | series-reduced | simple | spider | split | spoke | square-free | stacked book | star | strongly perfect | tree | triangle-free | unigraphic | uniquely colorable | uniquely embeddable | uniquely graceful | unit-distance | unswitchable | untraceable | weakly perfect

6-complete graph and singleton

6-complete graph

vertex degrees | 1 (6 vertices) | 6 (1 vertex)

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

x^5 (x^2 - 6)

(x + 1)^6

x^6

chromatic number | 2 edge chromatic number | 6

(-sqrt(6))^1 0^5 sqrt(6)^1

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

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

Hosoya index | 7 Kirchhoff index | 36 stability index | 0 Wiener index | 36