PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: Very low Entry average rating: No information on entry rating
neighborhood (of a vertex) (Definition)

For a graph $ G$, the set of vertices adjacent to a vertex $ x \in G$, the neighborhood of $ x$, is denoted by $ \Gamma(x)$. Occasionally one calls $ \Gamma(x)$ the open neighborhood of $ x$, and $ \Gamma \cup \{x\}$ the closed neighborhood of $ x$.

Adapted with permission of the author from Modern Graph Theory by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.



"neighborhood (of a vertex)" is owned by digitalis.
(view preamble)

View style:

See Also: graph

Other names:  neighborhood
Keywords:  vertex, graph
Log in to rate this entry.
(view current ratings)

Cross-references: graph theory, closed, open, adjacent, vertices, graph
There are 93 references to this entry.

This is version 6 of neighborhood (of a vertex), born on 2001-11-12, modified 2002-03-07.
Object id is 785, canonical name is NeighborhoodOfAVertex.
Accessed 6831 times total.

Classification:
AMS MSC05C99 (Combinatorics :: Graph theory :: Miscellaneous)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)