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An articulation vertex of a connected graph, also called a cut-vertex (Harary 1994, p. 26; West 2000; Gross and Yellen 2006) or "cutpoint" (Harary 1994, p. 26), is a vertex ...

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 ...

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 ...

The Lovász number theta(G) of a graph G, sometimes also called the theta function of G, was introduced by Lovász (1979) with the explicit goal of estimating the Shannon ...

Let a set of vertices A in a connected graph G be called convex if for every two vertices x,y in A, the vertex set of every (x,y) graph geodesic lies completely in A. Also ...

The maximal independence polynomial I_G(x) for the graph G may be defined as the polynomial I_G(x)=sum_(k=i(G))^(alpha(G))s_kx^k, where i(G) is the lower independence number, ...

The maximal irredundance polynomial R_G(x) for the graph G may be defined as the polynomial R_G(x)=sum_(k=ir(G))^(IR(G))r_kx^k, where ir(G) is the (lower) irredundance ...

The maximal matching-generating polynomial M_G(x) for the graph G may be defined as the polynomial M_G(x)=sum_(k=nu_L(G))^(nu(G))m_kx^k, where nu_L(G) is the lower matching ...

The unique 8_3 configuration. It is transitive and self-dual, but cannot be realized in the real projective plane. Its Levi graph is the Möbius-Kantor graph.

An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...