2. If a binary tree has 19 vertices then list out the number of vertices having degree 1, degree
2 and degree 3 .
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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
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...
s children nodes Finding the specific od'sbothers DAodging whether the specifie node is leaf or by the adjacent matrix, then the matrix gr Gwith n vertices, ㅲt is 10. Ifthe binary tree is stored by the Judge if the node is on the same level D Find the node position acording to its eenial method, which operation is easy to implement? 10 l Answer are Il True or False ( 10 POINTS) 2. The insertion and deletion 3. Sequential storage...
Please answer question 2. Introduction to Trees Thank you 1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
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?
ced binary tree is a binary tree where for each vertex the heights and right subtrees of that vertex differ by at most one. Let binary tree of tr s. A balanced the minimum number of vertices in a balanced Vn denote height n. (a) (4 points) Show that on satisfies for n 2 2 the recurrence on -1+ Un-2 ced binary tree is a binary tree where for each vertex the heights and right subtrees of that vertex differ...
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...
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).
COMP Discrete Structures: Please answer completely and clearly. (3). (5). x) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k possible colors to each of the vertices/edges of G so that adjacent vertices/edges have different colors. Draw pictures of each of the following (a) A 4-coloring of the edges of the Petersen graph. (b) A 3-coloring of the vertices of the Petersen graph. (e) A 2-coloring (d) A...