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A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, ...

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

A non-Abelian group, also sometimes known as a noncommutative group, is a group some of whose elements do not commute. The simplest non-Abelian group is the dihedral group ...

A graph with minimum vertex degree at least 5 is a line graph iff it does not contain any of the above six graphs, known in this work as Metelsky graphs, as an induced ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

A straight line embedding, or "straight line drawing," of a graph is a graph embedding in which all edges are drawn as straight line segments (as opposed to curves, etc.).

A simple graph is a line graph of some simple graph iff if does not contain any of the above nine graphs, known in this work as Beineke graphs, as a forbidden induced ...

There are four strongly regular graphs with parameters (nu,k,lambda,mu)=(28,12,6,4), one of them being the triangular graph of order 8. The other three such graphs are known ...