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A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n ...

The contraction of a pair of vertices v_i and v_j of a graph, also called vertex identification, is the operation that produces a graph in which the two nodes v_1 and v_2 are ...

A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z)=sum_(i=0)^inftyg_iz^i, (1) be the generating ...

The Goldberg graphs are a family of graphs discovered by Goldberg (1981) which are snarks for n=5, 7, 9, .... Precomputed properties of Goldberg graphs are implemented in the ...

The Mathon graphs are three strongly regular graphs on 784 vertices with regular parameters as summarized in the following tables. k spectrum regular parameters 0 ...

A tripod is a tree having exactly three tree leaves (Pirnazar and Ullman 2002). The numbers of tripods on n=1, 2, ... vertices are 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, ...

For s>1, the Riemann zeta function is given by zeta(s) = sum_(n=1)^(infty)1/(n^s) (1) = product_(k=1)^(infty)1/(1-1/(p_k^s)), (2) where p_k is the kth prime. This is Euler's ...

A prime magic square is a magic square consisting only of prime numbers (although the number 1 is sometimes allowed in such squares). The left square is the 3×3 prime magic ...

An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and ...