5. (a) Consider the trees with 17 vertices which have exactly 3 leaves. (i) Prove that any such tree must have a unique vertex of degree 3. (ii) Find the number of isomorphism classes of such trees in which the unique vertex of degree 3 is adjacent to a leaf. (b) A tree has a vertex of degree 3 and a vertex of degree 4. What is the minimum possible number of vertices in such a tree? Justify your answer. (c) Calculate the number of spanning trees for the following graph and explain your calculation: 6 D 5 2 3
5. (a) Consider the trees with 17 vertices which have exactly 3 leaves. (i) Prove that any such tree must have a unique vertex of degree 3. (ii) Find the number of isomorphism classes of such trees in which the unique vertex of degree 3 is adjacent to a leaf. (b) A tree has a vertex of degree 3 and a vertex of degree 4. What is the minimum possible number of vertices in such a tree? Justify your answer. (c) Calculate the number of spanning trees for the following graph and explain your calculation: 6 D 5 2 3
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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