S_6

(1, 5)-complete 2-partite graph | (1, 5)-complete bipartite graph | 1-tree (6, 6) | (5, 1)-Cayley tree | (5, 1)-spoke graph | (5, 1)-stacked book graph | 5-matchstick graph 5 | 6-edge-transitive graph 18 | 6-graph 6 | 6-tree 6 | 6-uniquely graceful graph 1

vertex count | 6 edge count | 5 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 | determined by spectrum | 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 | 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

pentatope and singleton

pentatope graph

vertex degrees | 1 (5 vertices) | 5 (1 vertex)

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

x^4 (x^2 - 5)

(x + 1)^5

x^5

chromatic number | 2 edge chromatic number | 5

(-sqrt(5))^1 0^4 sqrt(5)^1

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

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

Hosoya index | 6 Kirchhoff index | 25 stability index | 6 Wiener index | 25