singleton graph | 3-path graph | claw graph | 5-star graph | 6-star graph | complete binary tree of depth 3 | 7-star graph | 8-star graph | 9-star graph | 10-star graph | 11-star graph | 12-star graph | complete ternary tree of depth 3 | 13-star graph | 14-star graph | complete binary tree of depth 4 | 15-star graph | 16-star graph | 17-star graph | 18-star graph | ... (total: 27)

0-hypercube graph | 0-triangular grid graph | (1, 0)-permutation star graph | (1, 1, 1, 1)-grid graph | (1, 1, 1)-grid graph | (1, 1)-antelope graph | (1, 1)-bishop graph | (1, 1)-black bishop graph | (1, 1)-camel graph | (1, 1)-fiveleaper graph | ...

(1, 1, 3)-grid graph | (1, 2)-complete 2-partite graph | (1, 2)-complete bipartite graph | (1, 2)-Sierpiński simplex graph | (1, 3)-king graph | (2, 1)-stacked book graph | (2, 3)-black bishop graph | (2, 3)-white bishop graph | 2-Fibonacci cube graph | 2-matchstick graph 1 | ...

(1, 3)-complete 2-partite graph | (1, 3)-complete bipartite graph | (3, 1)-Cayley tree | (3, 1)-stacked book graph | 3-matchstick graph 2 | 4-edge-transitive graph 4 | 4-graph 4 | 4-star graph | 4-tree 2 | Y graph

(1, 4)-complete 2-partite graph | (1, 4)-complete bipartite graph | 1-alkane graph | 1-n-alkane graph | (4, 1)-Cayley tree | (4, 1)-stacked book graph | 4-matchstick graph 2 | 5-edge-transitive graph 12 | 5-graph 5 | 5-tree 4 | ...

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

6-matchstick graph 25 | 7-graph 38 | 7-tree 10

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

(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

(1, 8)-complete 2-partite graph | (1, 8)-complete bipartite graph | (8, 1)-Cayley tree | (8, 1)-stacked book graph | 8-matchstick graph 107 | 9-edge-transitive graph 11 | 9-graph 9 | 9-tree 47

10-edge-transitive graph 14 | 10-graph 10 | 10-tree 106 | (1, 9)-complete 2-partite graph | (1, 9)-complete bipartite graph | (9, 1)-Cayley tree | (9, 1)-stacked book graph | 9-matchstick graph 358

| vertex count | edge count | connected component count singleton graph | 1 | 0 | 1 3-path graph | 3 | 2 | 1 claw graph | 4 | 3 | 1 5-star graph | 5 | 4 | 1 6-star graph | 6 | 5 | 1 complete binary tree of depth 3 | 7 | 6 | 1 7-star graph | 7 | 6 | 1 8-star graph | 8 | 7 | 1 9-star graph | 9 | 8 | 1 10-star graph | 10 | 9 | 1

acyclic | apex | bicolorable | bipartite | cactus | chordal | chordless | class 1 | complete tree | connected | forest | geodetic | matchstick | median | no perfect matching | outerplanar | perfect | planar | projective planar | pseudoforest | pseudotree | simple | square-free | tree | triangle-free | uniquely colorable | unit-distance | weakly perfect

| complement graph name singleton graph | singleton graph 3-path graph | 2-path and singleton claw graph | triangle and singleton 5-star graph | tetrahedron and singleton 6-star graph | pentatope and singleton

| line graph name singleton graph | null graph 3-path graph | 2-path graph claw graph | triangle graph 5-star graph | tetrahedral graph 6-star graph | pentatope graph