Editing Glossary of graph theory (section)

==R==
{{glossary}}

{{term|radius}}
{{defn|The radius of a graph is the minimum {{gli|eccentricity}} of any vertex.}}

{{term|Ramanujan}}
{{defn|A [[Ramanujan graph]] is a graph whose spectral expansion is as large as possible. That is, it is a {{mvar|d}}-regular graph, such that the second-largest eigenvalue of its adjacency matrix is at most <math>2\sqrt{d-1}</math>.}}

{{term|ray}}
{{defn|A ray, in an infinite graph, is an infinite simple path with exactly one endpoint. The [[End (graph theory)|ends]] of a graph are equivalence classes of rays.}}

{{term|reachability|[[reachability]]}}
{{defn|The ability to get from one {{gli|vertex}} to another within a {{gli|graph}}.}}

{{term|reachable}}
{{defn|Has an affirmative {{gli|reachability}}. A {{gli|vertex}} {{math|''y''}} is said to be reachable from a vertex {{math|''x''}} if there exists a {{gli|path}} from {{math|''x''}} to {{math|''y''}}.}}

{{term|recognizable}}
{{defn|In the context of the [[reconstruction conjecture]], a graph property is recognizable if its truth can be determined from the deck of the graph. Many graph properties are known to be recognizable. If the reconstruction conjecture is true, all graph properties are recognizable.}}

{{term|reconstruction}}
{{defn|The [[reconstruction conjecture]] states that each undirected graph {{mvar|G}} is uniquely determined by its ''deck'', a multiset of graphs formed by removing one vertex from {{mvar|G}} in all possible ways. In this context, reconstruction is the formation of a graph from its deck.}}

{{term|rectangle}}
{{defn|A simple cycle consisting of exactly four edges and four vertices.}}

{{term|regular}}
{{defn|A graph is {{mvar|d}}-regular when all of its vertices have degree {{mvar|d}}. A [[regular graph]] is a graph that is {{mvar|d}}-regular for some {{mvar|d}}.}}

{{term|regular tournament}}
{{defn|A regular tournament is a tournament where in-degree equals out-degree for all vertices.}}

{{term|reverse}}
{{defn|See {{gli|transpose}}.}}

{{term|root}}
{{defn|no=1|A designated vertex in a graph, particularly in directed trees and [[rooted graph]]s.}}
{{defn|no=2|The inverse operation to a [[graph power]]: a {{mvar|k}}th root of a graph {{mvar|G}} is another graph on the same vertex set such that two vertices are adjacent in {{mvar|G}} if and only if they have distance at most {{mvar|k}} in the root.}}

{{glossary end}}