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The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

The EKG sequence is the integer sequence having 1 as its first term, 2 as its second, and with each succeeding term being the smallest number not already used that shares a ...

The Earls sequence gives the starting position in the decimal digits of pi (or in general, any constant), not counting digits to the left of the decimal point, at which a ...

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges lambda(G) whose deletion from a graph G disconnects G. In other words, it ...

Let c_k be the number of edge covers of a graph G of size k. Then the edge cover polynomial E_G(x) is defined by E_G(x)=sum_(k=0)^mc_kx^k, (1) where m is the edge count of G ...

Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

For any Abelian group G and any natural number n, there is a unique space (up to homotopy type) such that all homotopy groups except for the nth are trivial (including the ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...