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For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.

The join G=G_1+G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph union G_1 union G_2 together with all the edges joining ...

An empty graph on n nodes consists of n isolated nodes with no edges. Such graphs are sometimes also called edgeless graphs or null graphs (though the term "null graph" is ...

The dodecadodecahedral graph is the skeleton of the dodecadodecahedron, great dodecahemicosahedron, and small dodecahemicosahedron. It is illustrated above in several ...

A column-convex self-avoiding polygon which contains the bottom edge of its minimal bounding rectangle. The anisotropic perimeter and area generating function ...

A cyclic graph is a graph containing at least one graph cycle. A graph that is not cyclic is said to be acyclic. A cyclic graph possessing exactly one (undirected, simple) ...

The 13 Archimedean dual graphs are the skeletons of the Archimedean dual solids, illustrated above. Since they are polyhedral graphs, they are also planar. However, none of ...

The neighborhood graph of a given graph from a vertex v is the subgraph induced by the neighborhood of a graph from vertex v, most commonly including v itself. Such graphs ...

A quintic graph is a graph which is 5-regular. The only quintic graph on n<=7 nodes is the complete graph K_6. Quintic graphs exist only on even numbers of nodes, and the ...

The Hatzel graph is a planar hypohamiltonian graph on 57 vertices that was the smallest known example of such a graph until the discovery of the Zamfirescu graph on 48 ...