4. (a) Let T be a tree with 50 edges. The removal of certain edge from T yields two disjoint trees T1 and T2. Given that the number of vertices in T1 equals the number of edges in T2, determine the number of vertices and the number of edges in T1 and T2.Also, show that a regular binary tree has an odd number of vertices.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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4. (a) Let T be a tree with 50 edges. The removal of certain edge from T yields two disjoint
trees T1 and T2. Given that the number of vertices in T1 equals the number of edges in
T2, determine the number of vertices and the number of edges in T1 and T2.Also, show
that a regular binary tree has an odd number of vertices.
(b) Define isomorphism between graphs? Check whether the following two graphs are
isomorphic or not. Justify your answer.
Transcribed Image Text:4. (a) Let T be a tree with 50 edges. The removal of certain edge from T yields two disjoint trees T1 and T2. Given that the number of vertices in T1 equals the number of edges in T2, determine the number of vertices and the number of edges in T1 and T2.Also, show that a regular binary tree has an odd number of vertices. (b) Define isomorphism between graphs? Check whether the following two graphs are isomorphic or not. Justify your answer.
(b) Define isomorphism between graphs? Check whether the following two graphs
isomorphic
are
or not. Justify your answer.
Transcribed Image Text:(b) Define isomorphism between graphs? Check whether the following two graphs isomorphic are or not. Justify your answer.
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