4. Let T be a tree with n ≥ 1 vertices. (a) Show that T has a vertex of degree 1.
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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Transcribed Image Text:4. Let T be a tree with n ≥ 1 vertices.
(a) Show that I has a vertex of degree 1.
(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.
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