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edge
Author: Marian Olejar, Jr. Created: Apr/11/2006 Last edit: Oct/23/2006
other names: arc, curve, curved arc
graph theory: Edges are elements of edge set E in graph G=(V, E). They are two-element subsets of set V (vertex set). An edge is an (connected) unordered pair of distinct verices of G. It is also a 1D cell of a complex. Edge must have 2 or 1 ends (endverices, endpoints). Set of ends is sometimes called endpoint set. If edge has 2 ends, it is "most common type of edge" and it looks like this:
If edge has 1 end, it is called loop. The edge set of graph G is referred to as E(G). An edge e = {u, v}, where u, v`in`V is usually written as uv, e = uv. If uv is an edge, then we say that u and v are adjacent edges or u is neighbour of v. The edges of simple graph in `RR^3` are 1-simplexes. See also: incident, Further reading: 1. Diestel, Reinhard: Graph Theory, Graduate Texts in Mathematics, Springer, 2005, ISBN: 3540261826 2. Godsil, Chris; Royle, Gordon: Algebraic Graph Theory, Graduate Texts in Mathematics, Springer, 2001, ISBN: 0387952209 3. Gross, Jonathan L.; Tucker, Thomas W.: Topological Graph Theory, Dover Publications, 2001, ISBN: 0486417417 Cite this article as: Marian Olejar, Jr.: edge from VeryPrime's Dictionary of mathematics Link to this page: http://www.veryprime.com/dict/edge.php |