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An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

A graph is a forbidden subgraph if its presence as a subgraph of a given graph means it is not a member of some family of graphs. For example, a bipartite graph is a graph ...

A graph is a forbidden topological minor (also known as a forbidden homeomorphic subgraph) if its presence as a homeomorphic subgraph of a given graph (i.e., there is an ...

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

The sequence of graphs starting with the Suzuki graph and successively taking local graphs, summarized in the following table, is known as the Suzuki tower, a name due to ...

The Hamiltonian number h(n) of a connected graph G is the length of a Hamiltonian walk G. In other words, it is the minimum length of a closed spanning walk in the graph. For ...