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The clique covering number theta(G) of a graph G is the minimum number of cliques in G needed to cover the vertex set of G. Since theta(G) involves the minimum number of ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

The vertex cover number is the size of a minimum vertex cover in a graph G is known as the vertex cover number of G, denoted tau(G). The König-Egeváry theorem states that the ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...

The heptanacci numbers are a generalization of the Fibonacci numbers defined by H_0=0, H_1=1, H_2=1, H_3=2, H_4=4, H_5=8, H_6=16, and the recurrence relation ...

The hexanacci numbers are a generalization of the Fibonacci numbers defined by H_0=0, H_1=1, H_2=1, H_3=2, H_4=4, H_5=8, and the recurrence relation ...

A "visual representation" number which is a sum of some simple function of its digits. For example, 1233 = 12^2+33^2 (1) 2661653 = 1653^2-266^2 (2) 221859 = 22^3+18^3+59^3 ...

Perfect numbers are positive integers n such that n=s(n), (1) where s(n) is the restricted divisor function (i.e., the sum of proper divisors of n), or equivalently ...

Numbers which are not perfect and for which s(N)=sigma(N)-N<N, or equivalently sigma(n)<2n, where sigma(N) is the divisor function. Deficient numbers are sometimes called ...

A figurate number of the form g_n=2n-1 giving the area of the square gnomon obtained by removing a square of side n-1 from a square of side n, g_n = n^2-(n-1)^2 (1) = 2n-1. ...