Structures for complete undirected graphs, Data Structure & Algorithms

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.

Posted Date: 7/10/2012 4:26:42 AM | Location : United States







Related Discussions:- Structures for complete undirected graphs, Assignment Help, Ask Question on Structures for complete undirected graphs, Get Answer, Expert's Help, Structures for complete undirected graphs Discussions

Write discussion on Structures for complete undirected graphs
Your posts are moderated
Related Questions
Write a program that uses the radix sort to sort 1000 random digits. Print the data before and after the sort. Each sort bucket should be a linked list. At the end of the sort, the

So far, we now have been concerned only with the representation of single stack. What happens while a data representation is required for several stacks? Let us consider an array X

the above title please send give for the pdf file and word file

what do you understand by structured programming?explain with eg. top down and bottem up programming technique

Normally a potential y satisfies y r = 0 and 0 ³ y w - c vw -y v . Given an integer K³0, define a K-potential to be an array y that satisfies yr = 0 and K ³ y w - c vw -y v

Define Prim's Algorithm Prim's  algorithm  is  a  greedy  algorithm  for  constructing  a  minimum  spanning  tree  of  a  weighted linked graph. It works by attaching to a bef

how to implement prims algorithm dynamically

This question deals with AVL trees. You must use mutable pairs/lists to implement this data structure: (a) Define a procedure called make-avl-tree which makes an AVL tree with o

Q. Implement a stack making use of the linked list. Show the PUSH and POP operations both. A n s . Stack implemantation using linked list # include # include

Explain the Assertions in Ruby Ruby offers no support for assertions whatever. Moreover, because it's weakly typed, Ruby doesn't even enforce rudimentary type checking on opera