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List of graphs
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.
The strongly regular graph on v vertices and rank k is usually denoted srg(v,k,λ,μ).
A symmetric 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 complete graph on vertices is often called the -clique and usually denoted , from German komplett.
The complete bipartite graph is usually denoted . For see the section on star graphs. The graph equals the 4-cycle (the square) introduced below.
The cycle graph on 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.
The friendship graph Fn can be constructed by joining n copies of the cycle graph C3 with a common vertex.
In graph theory, a fullerene is any polyhedral 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.
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List of graphs
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.
The strongly regular graph on v vertices and rank k is usually denoted srg(v,k,λ,μ).
A symmetric 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 complete graph on vertices is often called the -clique and usually denoted , from German komplett.
The complete bipartite graph is usually denoted . For see the section on star graphs. The graph equals the 4-cycle (the square) introduced below.
The cycle graph on 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.
The friendship graph Fn can be constructed by joining n copies of the cycle graph C3 with a common vertex.
In graph theory, a fullerene is any polyhedral 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.