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An edge cut (Holton and Sheehan 1993, p. 14; West 2000, p. 152), edge cut set, edge cutset (Holton and Sheehan 1993, p. 14), or sometimes simply "cut set" or "cutset" (e.g., ...

A bridge of a connected graph is a graph edge whose removal disconnects the graph (Chartrand 1985, p. 45; Skiena 1990, p. 177). More generally, a bridge is an edge of a ...

The biconnected graph theta_0 on seven nodes and seven edges illustrated above. It has chromatic polynomial pi_(theta_0)(z)=z^7-8z^6+28z^5-56z^4+68z^3-47z^2+14z and chromatic ...

A cactus graph, sometimes also called a cactus tree, a mixed Husimi tree, or a polygonal cactus with bridges, is a connected graph in which any two graph cycles have no edge ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

A compactum (plural: compacta) is a compact metric space. An example of a compactum is any finite discrete metric space. Also, the space [0,1] union [2,3] is a compactum, ...

A set in R^d is concave if it does not contain all the line segments connecting any pair of its points. If the set does contain all the line segments, it is called convex.

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

Let N be a nilpotent, connected, simply connected Lie group, and let D be a discrete subgroup of N with compact right quotient space. Then N/D is called a nilmanifold.