grapii wi tnat пave degree o and the remaining two have degree 4? If yes, then draw the graph and if not, then prove

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.5: Convex Polygons
Problem 41E
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(a) Is there an undirected graph with 7 vertices such that five of the vertices have degree 3
and the remaining two have degree 4? If yes, then draw the graph and if not, then prove
your answer.
In the following, let T denote a full 3-ary (rooted) tree with 25 vertices. Justify your answers
co the questions below.
(b) Find the number of internal vertices (denote it by i) and the number of leaves of T (denote
it by l).
(c) What is the minimum possible height for T?
(d) If T is balanced, then what is the height of T?
Transcribed Image Text:(a) Is there an undirected graph with 7 vertices such that five of the vertices have degree 3 and the remaining two have degree 4? If yes, then draw the graph and if not, then prove your answer. In the following, let T denote a full 3-ary (rooted) tree with 25 vertices. Justify your answers co the questions below. (b) Find the number of internal vertices (denote it by i) and the number of leaves of T (denote it by l). (c) What is the minimum possible height for T? (d) If T is balanced, then what is the height of T?
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