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A (p,q)-graph is edge-graceful if the edges can be labeled 1 through q in such a way that the labels induced on the vertices by summing over incident edges modulo p are ...

Tait's Hamiltonian graph conjecture asserted that every cubic polyhedral graph is Hamiltonian. It was proposed by Tait in 1880 and refuted by Tutte (1946) with a ...

The Wolfram Physics Project posits the existence of abstract relations between atoms of space whose pattern defines the structure of physical space. In this approach, two ...

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

The smallest cubic graphs with graph crossing number CN(G)=n have been termed "crossing number graphs" or n-crossing graphs by Pegg and Exoo (2009). The n-crossing graphs are ...

A column-convex self-avoiding polygon which contains the bottom edge of its minimal bounding rectangle. The anisotropic perimeter and area generating function ...

A generalized dodecagon is a generalized polygon of order 12. GD(1,2) is the (3,12)-cage graph, more commonly known as the Tutte 12-cage. GD(2,1) is the line graph of the ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 and m=2,3, but only a small ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...