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The distance d(v, w) between two vertices v and w in an undirected graph is defined as the minimal length of any path connecting these two vertices. If v and w are not connected, then d(v, w) = ∞. Now, define the diameter of the graph G = (V, E) as diam(G) = max d(v,w). v,wɛV And define the radius of the graph as rad(G) = min max d(v, w) . veV weV Prove that rad(G) < diam(G) < 2rad(G).

The distance d(v, w) between two vertices v and w in an undirected graph is defined as the minimal length of any path connecting these two vertices. If v and w are not connected, then d(v, w) = ∞. Now, define the diameter of the graph G = (V, E) as diam(G) = max d(v,w). v,wɛV And define the radius of the graph as rad(G) = min max d(v, w) . veV weV Prove that rad(G) < diam(G) < 2rad(G).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Question Distance in graphs (02). The distance d(v, w) between two vertices v and w in an undirected graph is defined as the minimal length of any path connecting these two vertices. If v and w are not connected, then d(v, w) = o. Now, define the diameter of the graph G = (V, E) as diam(G) = max d(v, w). v, wEV And define the radius of the graph as rad(G) = min max d(v, w) vEV wEV Prove that rad(G) < diam(G) < 2rad(G).
Transcribed Image Text:Question Distance in graphs (02). The distance d(v, w) between two vertices v and w in an undirected graph is defined as the minimal length of any path connecting these two vertices. If v and w are not connected, then d(v, w) = o. Now, define the diameter of the graph G = (V, E) as diam(G) = max d(v, w). v, wEV And define the radius of the graph as rad(G) = min max d(v, w) vEV wEV Prove that rad(G) < diam(G) < 2rad(G).
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