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The connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

The cross number of a zero-system sigma={g_1,g_2,...,g_n} of G is defined as K(sigma)=sum_(i=1)^n1/(|g_i|) The cross number of a group G has two different definitions. 1. ...

A method of determining the maximum number of positive and negative real roots of a polynomial. For positive roots, start with the sign of the coefficient of the lowest (or ...

The Dirichlet kernel D_n^M is obtained by integrating the number theoretic character e^(i<xi,x>) over the ball |xi|<=M, D_n^M=-1/(2pir)d/(dr)D_(n-2)^M.

A snark on 30 vertices with edge chromatic number 4. It is implemented in the Wolfram Language as GraphData["DoubleStarSnark"].

If an infinite number of points in the plane are all separated by integer distances, then all the points lie on a straight line.

A sequence {a_1,a_2,a_3,...} fulfils a given property eventually if it fulfils it from some point onward, or, more precisely, if the property is fulfilled by the subsequence ...

Fatou dust is a Fatou set for a point outside the underlying set. Such a set has zero area and has an infinite number of disconnected components.

The only whole number solution to the Diophantine equation y^3=x^2+2 is y=3, x=+/-5. This theorem was offered as a problem by Fermat, who suppressed his own proof.

A smooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes ...