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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 ...

Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

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 ...

Let G_1, G_2, ..., G_t be a t-graph edge coloring of the complete graph K_n, where for each i=1, 2, ..., t, G_i is the spanning subgraph of K_n consisting of all graph edges ...

A polyhedron that is dual to itself. For example, the tetrahedron is self-dual. Naturally, the skeleton of a self-dual polyhedron is a self-dual graph. Pyramids are ...

An edge cover is a subset of edges defined similarly to the vertex cover (Skiena 1990, p. 219), namely a collection of graph edges such that the union of edge endpoints ...