Friendship Graph
In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or -fan) is a planar, undirected graph with vertices and edges. The friendship graph can be constructed by joining copies of the cycle graph with a common vertex, which becomes a universal vertex for the graph. By construction, the friendship graph is isomorphic to the windmill graph . It is unit distance with girth 3, diameter 2 and radius 1. The graph is isomorphic to the butterfly graph. Friendship theorem The friendship theorem of states that the finite graphs with the property that every two vertices have exactly one neighbor in common are exactly the friendship graphs. Informally, if a group of people has the property that every pair of people has exactly one friend in common, then there must be one person who is a friend to all the others. However, for infinite graphs, there can be many different graphs with the same cardinality that have this property. A combinatorial ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Friendship Graph 8
Friendship is a relationship of mutual affection between people. It is a stronger form of interpersonal bond than an "acquaintance" or an "association", such as a classmate, neighbor, coworker, or colleague. In some cultures, the concept of friendship is restricted to a small number of very deep relationships; in others, such as the U.S. and Canada, a person could have many friends, plus perhaps a more intense relationship with one or two people, who may be called ''good friends'' or ''best friends''. Other colloquial terms include ''besties'' or '' Best Friends Forever'' (''BFF''s). Although there are many