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The nth-order Menger sponge graph is the connectivity graph of cubes in the nth iteration of the Menger sponge fractal. The first two iterations are shown above. The n-Menger ...

An asymmetrical apodization function defined by M(x,b,d)={0 for x<-b; (x-b)/(2b) for -b<x<b; 1 for b<x<b+2d; 0 for x<b+2d, (1) where the two-sided portion is 2b long (total) ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

A minimal edge cover is an edge cover of a graph that is not a proper subset of any other edge cover. Every minimum edge cover is a minimal edge cover, but the converse does ...

A minimal vertex cut is an vertex cut of a graph that is not a proper subset of any other vertex cut. Every minimum vertex cut is a minimal vertex cut, but the converse does ...

A minimum clique covering is a clique covering of minimum size, and the size of such a minimum clique covering is known as the clique covering number. Note that while a ...

A minimum dominating set is a dominating set of smallest size in a given graph. The size of a minimum dominating set is known as the domination number of the graph. A minimum ...

The minimum leaf number ml(G) of a connected graph G is the smallest number of tree leaves in any of its spanning trees. (The corresponding largest number of leaves is known ...

Let f be analytic on a domain U subset= C, and assume that f never vanishes. Then if there is a point z_0 in U such that |f(z_0)|<=|f(z)| for all z in U, then f is constant. ...

The minimum vertex degree, sometimes simply called the minimum degree, of a graph G is the smallest vertex degree of G, denoted delta.