1 the degreev of a pendant vertex may be either one or

Assignment Help Computer Engineering
Reference no: EM13346325

1. The degree(v) of a pendant vertex may be either one or zero. 

     T  or  F 

2. A tree is any connected, undirected graph with an odd number of vertices. 

     T  or  F 

3. A simple graph is an undirected graph with multiple edges but no loops. 

     T  or  F 

4. A multigraph is an undirected graph with multiple edges and no loops. 

     T  or  F 

5. Consider the following directed relations on {1, 2, 3, 4} :

           R = {(1,1), (2,2), (3,3), (4,4)}

           S = {(1,4), (2,3), (3,2), (4,1)}

           R is reflexive and S is symmetric

     T  or  F

6.  Set A is divided into several disjoint partitions.  The UNION of these partitions is the original set.

     T  or  F

7. A W23 has 24 vertices and 46 edges. 

     T  or  F

8. The root of any tree must be at either level 1 (one) or level 0 (zero). 

     T  or  F 

9. A leaf is a vertex with just one child. 

     T  or  F 

10. A weighted graph has a value assigned to each edge. 

     T  or  F 

11. The minimum spanning tree of a weighted graph is a graph that

    is drawn with the length of each edge roughly proportional to

    the value assigned to each edge. 

     T  or  F 

12. Siblings must have the same parent but not necessarily the same level. 

     T  or  F 

13. Since Prim's and Kruskal's algorithms generate the minimum spanning tree of a given weighted graph, each algorithm would always

    provide identical MST solutions. 

     T  or  F 

14. A bipartite graph Kn,m has (n+m) vertices and a maximum of

    (n*m) edges. 

     T  or  F

PART B

1. Form a binary search tree from the words of the following sentence using alphabetical order and inserting words as they appear in the sentence: 

   This test is easier than the last because it is much shorter. 

2. The expression below is in postfix expression form.  Determine its numerical value. 

      { -4,  6,  -,  7,  5,  *,  2,  *,  / }   

3. Determine if Graph Z is bipartite.  Defend your answer.

4. Define a postorder and preorder traversal of the following:

          [(3 - 2y) * 5 ] - [(y - 3) ^ 6) ]  . 

       a. postorder: 

       b. preorder: 

5. Determine the Minimal Spanning Tree in Graph X using Kruskal's

Algorithm.  All edges must be labeled from lower to higher named vertices, e.g., from "c" to "d" but not from "d" to "c".

6. Given the coding scheme:

     a:001, b:0001, e:1, r:0000, s: 0100, t:011, x:01010

   Find the words represented by:  (1 point each)

   a. 0010000011

   b. 001010101

   c. 01110100011

   d. 0001110000

   e. What is the best compression ratio (versus ASCII 8-bit encoding) of the words in a through d above? (2 points).  Defend your answer.

7. Determine the Minimum Spanning Tree in Graph Y. Use Prim's Algorithm in which all edges must be labeled from lower to higher named vertices, e.g., from "c" to "d" but not from "d" to "c"

8. Construct a postorder, inorder and preorder transversal of Tree T.

    a. postorder:  

    b. inorder: 

    c: preorder: 

9. Are Graphs G and H isomorphic?  Defend your answer. 

10. Suppose that a full 41-ary tree has 4 internal vertices.  How many leaves does it have?  Defend your answer.

11. What is the shortest path in Graph S between "a" and "z".  Use Dijkstra's algorithm.

     a. the shortest path is: 

     b. the shortest distance between  "a"  and  "z"  is: 

12. A tree has 37 edges.  How many vertices does it have?

                  EXTRA CREDIT - OPTIONAL

DO ONE of the following: 

A.

Use a greedy algorithm to determine the shortest path in Graph S.  The algorithm starts at vertex "a" and ends at vertex "z" always selecting the shortest edge.  The selection must be in ascending lexicographic order, i.e., m to n  - not n to m.  See discussion on pages 195, 232, and 798.

B.

      Is the solution using Prim's Algorithm in Question B.5 the same topology and length as the required Kruskal solution?

 GRAPH  INFORMATION 

Graph G 

Initially draw a hexagon with vertices a-b-d-f-e-c-a. 

Connect vertices a to f; b to c; d to e. 

        b           d 

 

a                          f 

 

        c           e 

 

Graph H 

Initially draw a hexagon with vertices u-v-w-x-y-z-u. 

Connect vertices u to x; v to y; w to z. 

There is no connection in the center. 

                 u 

 

    z                         v 

 

 

    y                         w

                 x

Graph S 

Initially draw a hexagon with vertices a-b-d-z-e-c-a. 

Connect vertices b to c; b to e; c to d; d to e.

Edge values are: 

  a-b = 3; a-c = 4; 

  b-c = 1; b-d = 5; b-e = 5 

  c-d = 2; c-e = 4; 

  d-e = 1; d-z = 5; e-z = 3. 

 

             b            d 

 

    a                              z 

 

             c            e 

 

Tree T 

Construct a Tree with 

 vertex a at level 0; 

 vertices b, c and d at level 1; 

 vertices e, f, i, j, and k at level 2; 

 vertices g, h, l and m at level 3. 

Connect vertex a to b, a to c, and a to d. 

Connect vertex b to e and f. 

Connect vertex c (no further connection). 

Connect vertex d to i, j and k.

Connect vertex e to g.

Connect vertex f to h.  

Connect vertex i (no further connection).

Connect vertex j (no further connection).

Connect vertex k to l and m.

Connect vertex g, h, l and m (no further connection).

                 a 

 

       b         c         d 

 

    e     f           i    j    k 

 

    g     h                   l   m

 

Graph X 

Initially draw a rectangle with vertices a-c-e-z-d-b-a. 

Connect vertices a to d; c to d; d to e. 

Edge values are:  

  a-b = 1; a-c = 4; a-d =3; 

  b-d = 3; c-d = 3; c-e = 2; 

  d-e = 1; d-z = 2; e-z = 2. 

 

  a         c        e 

 

 

  b         d        z 

 

Graph Y 

Draw a hexagon with vertices a-b-d-z-e-c-a. 

Connect vertices b to c; b to z; d to e. 

Edge values are:

  a-b = 3; a-c = 5;

  b-c = 2; b-d = 5; b-z = 4;

  c-e = 5;

  d-e = 1; d-z = 7; e-z = 3. 

 

             b            d 

 

    a                              z 

 

             c            e 

 

Graph Z

Graph Z is a five-pointed figure.

Connect a to b, a to c and a to e.

Connect b to d.

Connect c to d.

Connect d to e.

 

           b            c

 

   a                             d

 

 

                 e

Reference no: EM13346325

Questions Cloud

Task 1 managing changeenacting change is difficult the : task 1 managing changeenacting change is difficult. the forces that create the need for change often bump up against
In this reprot you are to use movies video games tv shows : in this reprot you are to use movies video games tv shows or books graphic novels included to illustrate concepts from
1 solve the following linear programming problem : 1. solve the following linear programming problem graphicallymaximize 2x1 3x2subject to x1 le
Ahat is a ventures present value does the past matter : a.what is a ventures present value? does the past matter? what is meant by the statement if you are not using
1 the degreev of a pendant vertex may be either one or : 1. the degreev of a pendant vertex may be either one or zero.nbspnbspnbspnbspnbsp tnbsp ornbsp fnbsp2. a tree is any
Explain the construction of different types of power : explain the construction of different types of power transformer 1. explain with the aid of diagrams the following in
The shortest job next sjn algorithm queues processes in a : the shortest job next sjn algorithm queues processes in a way that the ones that use the shortest cpu cycle will be
A review full headers of a sample email message you : a. review full headers of a sample email message you received in your gmail account create one if you dont have one
Problem consider a trapezoidal piece of polymer film as : problem consider a trapezoidal piece of polymer film as shown below. the parallel sides of the trapezoid are insulated

Reviews

Write a Review

Computer Engineering Questions & Answers

  Mathematics in computing

Binary search tree, and postorder and preorder traversal Determine the shortest path in Graph

  Ict governance

ICT is defined as the term of Information and communication technologies, it is diverse set of technical tools and resources used by the government agencies to communicate and produce, circulate, store, and manage all information.

  Implementation of memory management

Assignment covers the following eight topics and explore the implementation of memory management, processes and threads.

  Realize business and organizational data storage

Realize business and organizational data storage and fast access times are much more important than they have ever been. Compare and contrast magnetic tapes, magnetic disks, optical discs

  What is the protocol overhead

What are the advantages of using a compiled language over an interpreted one? Under what circumstances would you select to use an interpreted language?

  Implementation of memory management

Paper describes about memory management. How memory is used in executing programs and its critical support for applications.

  Define open and closed loop control systems

Define open and closed loop cotrol systems.Explain difference between time varying and time invariant control system wth suitable example.

  Prepare a proposal to deploy windows server

Prepare a proposal to deploy Windows Server onto an existing network based on the provided scenario.

  Security policy document project

Analyze security requirements and develop a security policy

  Write a procedure that produces independent stack objects

Write a procedure (make-stack) that produces independent stack objects, using a message-passing style, e.g.

  Define a suitable functional unit

Define a suitable functional unit for a comparative study between two different types of paint.

  Calculate yield to maturity and bond prices

Calculate yield to maturity (YTM) and bond prices

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd