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1000=10^3. The word "thousand" appears in common expressions in a number of languages, for example, "a thousand pardons" in English and "tusen takk" ("a thousand thanks") in ...

The height of a tree g is defined as the vertex height of its root vertex, where the vertex height of a vertex v in a tree g is the number of edges on the longest downward ...

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 ...

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

By analogy with the divisor function sigma_1(n), let pi(n)=product_(d|n)d (1) denote the product of the divisors d of n (including n itself). For n=1, 2, ..., the first few ...

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 ...

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 ...

If, for n>=0, beta_n=sum_(r=0)^n(alpha_r)/((q;q)_(n-r)(aq;q)_(n+r)), (1) then beta_n^'=sum_(r=0)^n(alpha_r^')/((q;q)_(n-r)(aq;q)_(n+r)), (2) where alpha_r^' = ...

A chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...