Gallery of named graphs

From Wikipedia, the free encyclopedia

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.

1 Individual graphs
2 Graph families

[edit] Individual graphs

Triangle, $K 3$ , $C 3$ $n = 3$ , $m = 3$	Square, $C 4$ $n = 4$ , $m = 4$	Claw, $K 1,3$ , $S 4$ $n = 4$ , $m = 4$	Pentagon $n = 5$ , $m = 5$
Thomsen graph, Utility graph, $K 3,3$ $n = 6$ , $m = 9$	Cube $n = 8$	Octahedron $n = 8$	Brinkman graph
Clebsch graph	Dodecahedron $n = ?$ , $m = ?$	Flower snark	Icosahedron
Grötzsch graph	Tutte eight-cage	Heawood graph	Petersen graph
Szekeres snark	Thomassen graph

[edit] Graph families

[edit] Complete graphs

The complete graph on $n$ vertices is often called the $n$ -clique and usually denoted $K n$ , from German komplett. ^{[citation needed]}

$K 1$	$K 2$	$K 3$	$K 4$
$K 5$	$K 6$	$K 7$	$K 8$

[edit] Complete bipartite graphs

The complete bipartite graph is usually denoted $K n, m$

$K 3,1$

$K 3,2$

$K 3,3$

[edit] 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 $C 5$ .