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A square-free graph is a graph containing no graph cycles of length four. A simple graph is square-free iff c_4=1/8[Tr(A^4)-2m-2sum_(i!=j)a_(ij)^((2))]=0, where A is the ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

Three point geometry is a finite geometry subject to the following four axioms: 1. There exist exactly three points. 2. Two distinct points are on exactly one line. 3. Not ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p) and numbers are assigned to the edges of a grid. A b-cluster is an ...

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...

There are several definitions of "almost Hamiltonian" in use. As defined by Punnim et al. (2007), an almost Hamiltonian graph is a graph on n nodes having Hamiltonian number ...

A column-convex polyomino is a self-avoiding convex polyomino such that the intersection of any vertical line with the polyomino has at most two connected components. ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...