Let G be a tree with v vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the remaining vertices? Let G be a tree with v verti...
Can you draw the tree diagram for this please 12. Let T be a tree with 8 edges that has exactl 5 vertices of degree 1Prove that if v is a vertex of maximum degree in T, then 3 < deg(v) < 5 12. Let T be a tree with 8 edges that has exactl 5 vertices of degree 1Prove that if v is a vertex of maximum degree in T, then 3
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and all remaining vertices have degree 2. How many vertices does the graph have? 12 10 16 O 14
Suppose that T is a tree with four vertices of degree 3, six vertices of degree 4, one vertex of degree 5, and 8 vertices of degree 6. No other vertices of T have degree 3 or more. How many leaf vertices does T have?
Question 3. Draw a graph G = (V. E) on 10 nodes (vertices) with degrees 1.1.1.1.1.1.1.1.5, 5. V = {0, V2.03......}. Is G a tree? Why/why not? (Remember that a tree is a graph which is connected and has no cycles).
6. (a) Decide if there exists a full binary tree with twelve vertices. If so, draw the tree. If not explain why not. (b) Let G be a finite simple undirected graph in which each vertex has degree at least 2. Prove that G must contain a simple circuit (c) Let G be a graph with 2 vertices of degree 1, 3 of degree 2, and 2 of degree 3. Prove that G cannot be a tree
Sketch a tree T with 10 vertices where 4 vertices have degree 3 and 6 vertices have degree 1.
Use induction on n... 5. Use induction on n to prove that any tree on n2 2 vertices has at least two vertices of degree 1 (a vertex of degree 1 is called a leaf). 5. Use induction on n to prove that any tree on n2 2 vertices has at least two vertices of degree 1 (a vertex of degree 1 is called a leaf).
A tree with a vertex of degree k ≥ 1 has at least k vertices of degree 1.
Let T be a tree with 3 or more vertices. Prove the following: (a) There must be two vertices v, w in T that are not adjacent. (b) If T′ is the graph obtained from T by adding a new edge joining v to w, then T′ is not a tree.
Exercise 1 (a) Proof that (by an example with10) the number of terminal vertices in a binary tree with n vertices is (n 1)/2. (b) Give an example of a tree (n> 10) for which the diameter is not equal to the twice the radius. Find eccentricity, radius, diameter and center of the tree. (c) If a tree T has four vertices of degree 2, one vertex of degree 3, two vertices of degree 4, and one vertex of degree...