S_8

(1, 7)-complete 2-partite graph | (1, 7)-complete bipartite graph | (7, 1)-Cayley tree | (7, 1)-stacked book graph | 7-matchstick graph 35 | 8-edge-transitive graph 16 | 8-graph 8 | 8-tree 23

vertex count | 8 edge count | 7 connected component count | 1

acyclic | apex | asymmetric | bicolorable | bipartite | bridged | cactus | caterpillar | chordal | chordless | chromatically nonunique | class 1 | complete bipartite | complete k-partite | complete tree | connected | determined by resistance | determined by spectrum | edge-transitive | forest | geodetic | graceful | lobster | matchstick | median | noncayley | nonempty | noneulerian | nonhamiltonian | no perfect matching | outerplanar | perfect | planar | projective planar | pseudoforest | pseudotree | series-reduced | simple | spider | split | square-free | stacked book | star | strongly perfect | tree | triangle-free | uniquely colorable | unit-distance | untraceable | weakly perfect

7-complete graph and singleton

7-complete graph

vertex degrees | 1 (7 vertices) | 7 (1 vertex)

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

x^6 (x^2 - 7)

(x + 1)^7

x^7

chromatic number | 2 edge chromatic number | 7

(-sqrt(7))^1 0^6 sqrt(7)^1

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

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

Hosoya index | 8 Kirchhoff index | 49 stability index | 8 Wiener index | 49