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Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

A biplanar graph is defined as a graph that is the graph union of two planar edge-induced subgraphs. In other words, biplanar graphs are graphs with graph thickness 1 or 2 ...

The connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

A number traditionally associated with bad luck. A so-called baker's dozen is equal to 13. Fear of the number 13 is called triskaidekaphobia. There are 13 Archimedean solids. ...

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

The mapping of a grid of regularly ruled squares onto a cone with no overlap or misalignment. Cone nets are possible for vertex angles of 90 degrees, 180 degrees, and 270 ...