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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.

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.

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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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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