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单词 DistanceinAGraph
释义

distance (in a graph)


The distance d(x,y) of two vertices x and y of a graph G is the length of the shortest path (or, equivalently, walk) from x to y. If there is no path from x to y (i.e. if they lie in different components of G), we set d(x,y):=.

Two basic graph invariants involving distance are the diameter diamG:=max(x,y)V(G)2d(x,y) (the maximum distance between two vertices of G) and the radius radG:=minxV(G)maxyV(G)d(x,y) (the maximum distance of a vertex from a central vertex of G, i.e. a vertex such that the maximum distance to another vertex is minimal).

Titledistance (in a graph)
Canonical nameDistanceinAGraph
Date of creation2013-03-22 12:31:32
Last modified on2013-03-22 12:31:32
OwnerCWoo (3771)
Last modified byCWoo (3771)
Numerical id11
AuthorCWoo (3771)
Entry typeDefinition
Classificationmsc 05C12
Synonymdistance
Related topicGraph
Related topicPath
Related topicDiameter3
Related topicPathConnected
Definesdiameter (of a graph)
Definesradius (of a graph)
Definescentral vertex
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更新时间:2025/5/4 9:55:08