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The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs. The Goldner-Harary graph (Goldner and Harary 1975a, ...

A graph G is hypohamiltonian if G is nonhamiltonian, but G-v is Hamiltonian for every v in V (Bondy and Murty 1976, p. 61). The Petersen graph, which has ten nodes, is the ...

The McLaughlin graph is a 112-regular graph on 275 nodes and 15400 edges that can be constructed from the Witt design. It is distance-regular with intersection array ...

Origami is the Japanese art of paper folding. In traditional origami, constructions are done using a single sheet of colored paper that is often, though not always, square. ...

The Shrikhande graph is a strongly regular graph on 16 nodes. It is cospectral with the rook graph L_(4,4), so neither of the two is determined by spectrum. The Shrikhande ...

A space-filling polyhedron is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that ...

The mathematical study of the likelihood and probability of events occurring based on known information and inferred by taking a limited number of samples. Statistics plays ...

The signed Stirling numbers of the first kind are variously denoted s(n,m) (Riordan 1980, Roman 1984), S_n^((m)) (Fort 1948, Abramowitz and Stegun 1972), S_n^m (Jordan 1950). ...

The skeleton of the tesseract, commonly denoted Q_4, is a quartic symmetric graph with girth 4 and diameter 4. The automorphism group of the tesseract is of order 2^7·3=384 ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...