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Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

"The" Y-graph is another term used to refer to a claw graph. The term "Y-graph" is also used to refer to a graph expansion with the Y graph as its base (e.g., Horton and ...

For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

The difference of two numbers n_1 and n_2 is n_1-n_2, where the minus sign denotes subtraction.

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

The nth coefficient in the power series of a univalent function should be no greater than n. In other words, if f(z)=a_0+a_1z+a_2z^2+...+a_nz^n+... is a conformal mapping of ...

Bowling, known as "ten pins" throughout most of the world, is a game played by rolling a heavy ball down a long narrow track and attempting to knock down ten pins arranged in ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

Christoffel symbols of the second kind are the second type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. ...