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Tutte's (46-vertex) graph is a cubic nonhamiltonian graph contructed by Tutte (1946) as a counterexample to Tait's Hamiltonian graph conjecture by using three copies ...

The Wells graph, sometimes also called the Armanios-Wells graph, is a quintic graph on 32 nodes and 80 edges that is the unique distance-regular graph with intersection array ...

The Wiener-Araya graph (Wiener and Araya 2009) is the 42-vertex graph illustrated above that was the smallest known example of a planar hypohamiltonian graph, beating the ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

The associated Stirling numbers of the first kind d_2(n,k)=d(n,k) are defined as the number of permutations of a given number n having exactly k permutation cycles, all of ...

An incidence system (v, k, lambda, r, b) in which a set X of v points is partitioned into a family A of b subsets (blocks) in such a way that any two points determine lambda ...

Consider n strings, each oriented vertically from a lower to an upper "bar." If this is the least number of strings needed to make a closed braid representation of a link, n ...

Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

A discrete function A(n,k) is called closed form (or sometimes "hypergeometric") in two variables if the ratios A(n+1,k)/A(n,k) and A(n,k+1)/A(n,k) are both rational ...