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A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...

Grinberg constructed a number of small cubic polyhedral graph that are counterexamples to Tait's Hamiltonian graph conjecture (i.e., that every 3-connected cubic graph is ...

"The" H graph is the tree on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["HGraph"]. The term "H-graph" is also used to refer to a ...

A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, ...

For a sequence {chi_i}, the Levine-O'Sullivan greedy algorithm is given by chi_1 = 1 (1) chi_i = max_(1<=j<=i-1)(j+1)(i-chi_j) (2) for i>1. The sequence generated by this ...

The McGee graph is a cubic symmetric graph on 24 nodes and 36 edges which is the unique 7-cage graph. It can be constructed as the union of the two leftmost subgraphs ...

The Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

A nowhere-neat dissection is a dissection of an area into polygons such that no two polygons have a side in common. A nowhere-neat dissection in which squares of the same ...

A symbol employed in a formal propositional calculus.

The paw graph is the 3-pan graph, which is also isomorphic to the (3,1)-tadpole graph. It is implemented in the Wolfram Language as GraphData["PawGraph"].