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The pentakis icosidodecahedron is the dual of the chamfered dodecahedron. It contains 42 vertices, 120 edges, and 80 faces. The canonical version has two distinct edge ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

A trail is a walk v_0, e_1, v_1, ..., v_k with no repeated edge. The length of a trail is its number of edges. A u,v-trail is a trail with first vertex u and last vertex v, ...

The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function y=f(x). In particular, the segments of the diagram ...

If the rank polynomial R(x,y) of a graph G is given by sumrho_(rs)x^ry^s, then rho_(rs) is the number of subgraphs of G with rank r and co-rank s, and the matrix (rho_(rs)) ...

Riddell's formula for unlabeled graphs is the Euler transform relating the number of unlabeled connected graphs on n nodes satisfying some property with the corresponding ...

A Ramsey number of the form R(k,k;2).

It is conjectured that every tree with e edges whose nodes are all trivalent or monovalent can be given a "magic" labeling such that the integers 1, 2, ..., e can be assigned ...