Sketch a tree T with 10 vertices where 4 vertices have degree 3 and 6 vertices have degree 1.
Sketch a tree T with 10 vertices where 4 vertices have degree 3 and 6 vertices have degree 1.
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?
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 vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the remaining vertices?
1. If T is a tree with 999 vertices, then T has_edges (5 pts) 2. There are 3. The best comparison-based sorting algorithms for a list of n items have complexity ). (5 pts) 4. If T is a binary tree with 100 vertices, its minimum height is 5. If T is a full binary tree with 101 vertices, its maximum height is 6. If T is a full binary tree with 50 leaves, its minimum height is 7. Every...
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
4. (10 points) (a) An undirected graph has 6 vertices and 13 edges. It is known three vertices have degree 3, one has degree 4, and another one has degree 7. Find the degree of the remaining vertex. (b) For each of the following graphs, determine if it is bipartite, complete, and/or a tree. Give a brief written or graphical justification for your answers (you may address multiple graphs at the same time). iii.
A tree with a vertex of degree k ≥ 1 has at least k vertices of 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).
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...
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
Prove that a tree with at least two vertices must have at least one vertex of odd degree.