Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. A famous example is the Petersen graph, a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts. A labeled graph with 6 vertices and 7 edges. ...
The Petersen graph Another drawing of the Petersen graph, with only two crossings Another drawing, with each edge the same length The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory. ...
## Individual graphs
Triangle, *K*_{3}, *C*_{3} *n* = 3, *m* = 3 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| Square, *C*_{4} *n* = 4, *m* = 4 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| Claw, *K*_{1,3}, *S*_{4} *n* = 4, *m* = 4 In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set. ...
| Pentagon *n* = 5, *m* = 5 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| Thomsen graph, Utility graph, *K*_{3,3} *n* = 6, *m* = 9 Image File history File links Complete_bipartite_graph_K3,3. ...
| Fano plane Image:Fano. ...
A finite geometry is any geometric system that has only a finite number of points. ...
| Cube *n* = 8 In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
| | | | Dodecahedron *n* = ?, *m* = ? | Flower snark In graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to four. ...
| | | Levi graph, Tutte eight-cage Image File history File links Tutte_eight_cage. ...
| Heawood graph Image File history File links Heawood_graph. ...
| Petersen graph Image File history File links Petersen_graph. ...
The Petersen graph Another drawing of the Petersen graph, with only two crossings Another drawing, with each edge the same length The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory. ...
| | | ## Graph families ### Complete graphs The complete graph on *n* vertices is often called the *n*-clique and usually denoted *K*_{n}, from German *komplett*. ^{[citation needed]} In the mathematical field of graph theory a complete graph is a simple graph where an edge connects every pair of vertices. ...
| | | *K*_{4} Image File history File links Complete_graph_K4. ...
| *K*_{5} Image File history File links Complete_graph_K5. ...
| *K*_{6} Image File history File links Complete_graph_K6. ...
| | | ### Complete bipartite graphs The complete bipartite graph is ususally denoted *K*_{n,m} In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set. ...
*K*_{3,1} Image File history File links Complete_bipartite_graph_K3,1. ...
| *K*_{3,2} Image File history File links Complete_bipartite_graph_K3,2. ...
| *K*_{3,3} Image File history File links Complete_bipartite_graph_K3,3. ...
| ### Cycles The cycle graph on *n* vertices is called the *n-cycle* and usually denoted *C*_{n}. It is also called a *cyclic graph*, a *polygon* or the *n-gon*. Special cases are the *triangle* *C*_{3}, the *square* *C*_{4}, and the *pentagon* *C*_{5}. In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ...
### Star ### Wheel |