This partial list of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types, such as vertex and path, see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see Category:Graphs. 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.
Asymmetric graph is one in which there is a symmetry (graph automorphism) taking any ordered pair of adjacent vertices to any other ordered pair; the Foster census lists all small symmetric 3-regular graphs. Every strongly regular graph is symmetric, but not vice versa.
The cycle graphon vertices is called the n-cycle and usually denoted . It is also called a cyclic graph, a polygon or the n-gon. Special cases are the triangle, the square, and then several with Greek naming pentagon, hexagon, etc.
In graph theory, the term fullerene refers to any 3-regular, planar graph with all faces of size 5 or 6 (including the external face). It follows from Euler's polyhedron formula, V – E + F = 2 (where V, E, F indicate the number of vertices, edges, and faces), that there are exactly 12 pentagons in a fullerene and h = V/2 – 10 hexagons. Therefore V = 20 + 2h; E = 30 + 3h. Fullerene graphs are the Schlegel representations of the corresponding fullerene compounds.
An algorithm to generate all the non-isomorphic fullerenes with a given number of hexagonal faces has been developed by G. Brinkmann and A. Dress.[3] G. Brinkmann also provided a freely available implementation, called fullgen.
This partial list contains definitions of graphs and graph families which are known by particular names, but do not have a Wikipedia article of their own.
Agear graph, denoted Gn, is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a wheel graphWn. Thus, Gn has 2n+1 vertices and 3n edges.[4] Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs.[5] Gear graphs are also known as cogwheels and bipartite wheels.
The web graph Wn,r is a graph consisting of r concentric copies of the cycle graphCn, with corresponding vertices connected by "spokes". Thus Wn,1 is the same graph as Cn, and Wn,2 is a prism.
A web graph has also been defined as a prism graph Yn+1, 3, with the edges of the outer cycle removed.[7][10]
^Brinkmann, Gunnar; Dress, Andreas W.M (1997). "A Constructive Enumeration of Fullerenes". Journal of Algorithms. 23 (2): 345–358. doi:10.1006/jagm.1996.0806. MR1441972.
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