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An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

The pentatope graph is the skeleton of the pentatope, namely the complete graph K_5. It is sometimes also known as the Kuratowski graph (Nikolić et al. 2000, p. 281). Since ...

The theory of classifying problems based on how difficult they are to solve. A problem is assigned to the P-problem (polynomial-time) class if the number of steps needed to ...

The Petersen family of graphs, not to be confused with generalized Petersen graphs, are a set of seven graphs obtained from the Petersen graph (or complete graph K_6) by del ...

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 ...