The null graph or the empty graph is the graph with no points and no lines. The null graph is the initial object in the category of graphs. In mathematics, an initial object of a category C is an object I in C such that to every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object: T is terminal, if to every object X in C... In mathematics, categories allow one to formalize notions involving abstract structure and processes which preserve structure. ...

Graph theory is a growth area in mathematical research, and has a large specialized vocabulary. ...

References

Harary, F. and Read, R., "Is the Null Graph a Pointless Concept?", Graphs and Combinatorics Conference, George Washington University, Springer-Verlag, New York, NY, 1973.

In a weighted graph or digraph, each edge is associated with some value, variously called its cost, weight, length or other term depending on the application; such graphs arise in many contexts, for example in optimal route problems such as the traveling salesman problem.

Graph theory is the branch of mathematics that concerns itself with graphs.

Now, a (finite) graph is usually thought of as a subset of pairs of elements of a finite set (called vertices), or more generally as a family of arbitrary sets in the case of hypergraphs.

Share your thoughts, questions and commentary here

Want to know more? Search encyclopedia, statistics and forums:

Press Releases |
Feeds |
Contact
The Wikipedia article included on this page is licensed under the
GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms, 1022, m