Structures for complete undirected graphs, Data Structure & Algorithms

Assignment Help:

Q. Draw  the structures of complete  undirected  graphs  on  one,  two,  three,  four  and  five vertices also prove that the number of edges in an n vertex complete graph is n(n-1)/2.         

Ans:

The Graphs are drawn below:

i. Graph for One vertex:-

.A

ii. Graph for Two vertices:-

939_Undirected Graphs.png

2410_Graph for 2, 3, 5 vertices.png

From the above drawn Graphs we can see

i.     When n=1,

Then number of edges becomes

=n(n-1)/2

= 1(1-1)/2

=1(0)/2

=0/2

=0

Therefore, number of edges = 0. ii.   When n=2,

Then number of edges becomes

=n(n-1)/2

=2(2-1)/2

=2(1)/2

=2/2

=1

Therefore, number of edges = 1. iii. When n=3,

Then number of edges becomes

=n(n-1)/2

 

 

=3(3-1)/2

=3(2)/2

=6/2

=3

Therefore, number of edges becomes = 3.
 iv.   When n=4,

Then number of edges

=n(n-1)/2

=4(4-1)/2

=4(3)/2

=12/2

=6

Therefore, number of edges becomes = 6.
 v. When n=5,

Then number of edges becomes

=n(n-1)/2

=5(5-1)/2

=5(4)/2

=20/2

=10

Therefore, number of edges becomes = 10.


Related Discussions:- Structures for complete undirected graphs

Which sorting algorithm is adaptable to singly linked list, Which sorting a...

Which sorting algorithm is easily adaptable to singly linked lists? Simple Insertion sor t is easily adabtable to singly linked list.

Sparse matrix, Q. Define a sparse matrix. Explain different types of sparse...

Q. Define a sparse matrix. Explain different types of sparse matrices? Show how a triangular array is stored in memory. Evaluate the method to calculate address of any element ajk

Deletion from a red-black tree, Deletion in a RBT uses two main processes, ...

Deletion in a RBT uses two main processes, namely, Procedure 1: This is utilized to delete an element in a given Red-Black Tree. It involves the method of deletion utilized in

Algorithm to find maximum and minimum numbers, Give an algorithm to find bo...

Give an algorithm to find both the maximum and minimum of 380 distinct numbers that uses at most 568 comparisons.

Standard ways of traversing a graph, Q. Which are the two standard ways of ...

Q. Which are the two standard ways of traversing a graph?  Explain them with an example of each.  Ans:   T he two ways of traversing a graph are written below

Explain backtracking, Explain Backtracking The  principal idea is to co...

Explain Backtracking The  principal idea is to construct solutions single component  at a time  and evaluate such  partially constructed candidates as follows. If a partiall

General, whats the definition of ADT and data type?

whats the definition of ADT and data type?

Prims algorithm, how to write prims algorithms? with example

how to write prims algorithms? with example

Explain the term totalling, Explain the term totalling To add up a ser...

Explain the term totalling To add up a series numbers the subsequent type of statement must be used: Total = total + number  This literally means (new) total = (old) t

Write Your Message!

Captcha
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