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(b) Show that T has n - 1 edges. (c) Let G be a connected graph and suppose that e = {x,y} is an edge of G lying on a cycle. Show that G' = (V, E \ {e}) is connected. (d) Conclude that every connected graph on n vertices has a spanning tree.

(b) Show that T has n - 1 edges. (c) Let G be a connected graph and suppose that e = {x,y} is an edge of G lying on a cycle. Show that G' = (V, E \ {e}) is connected. (d) Conclude that every connected graph on n vertices has a spanning tree.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b,c,d

4. Let T be a tree with n> 1 vertices. (a) Show that T has a vertex of degree 1. (b) Show that I has n - 1 edges. (c) Let G be a connected graph and suppose that e = {x,y} is an edge of G lying on a cycle. Show that G' = (V, E \ {e}) is connected. (d) Conclude that every connected graph on n vertices has a spanning tree.
Transcribed Image Text:4. Let T be a tree with n> 1 vertices. (a) Show that T has a vertex of degree 1. (b) Show that I has n - 1 edges. (c) Let G be a connected graph and suppose that e = {x,y} is an edge of G lying on a cycle. Show that G' = (V, E \ {e}) is connected. (d) Conclude that every connected graph on n vertices has a spanning tree.
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