102ps1_07 - DEPARTMENT OF MATHEMATICS 102 FINITE...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
DEPARTMENT OF MATHEMATICS Problem Sheet 1 1. (a) Draw a graph with vertices v 1 , v 2 , v 3 and v 4 and edges ( v 1 , v 2 ) , ( v 1 , v 3 ) , ( v 2 , v 3 ) , ( v 2 , v 4 ) and ( v 4 , v 1 ). (b) Write down the number of edges, the degree of each vertex and the sum of the degrees of the vertices in the graph drawn. 2. The intersection graph of a collection of sets A 1 , A 2 , . . ., A n is the graph that has a vertex for each of these sets and has an edge connecting a pair of vertices if and only if the sets represented by these vertices have a non-empty intersection. (a) Construct the intersection graph of the following collection of sets: A 1 = { 0 , 2 , 4 , 6 , 8 } , A 2 = { 0 , 1 , 2 , 3 , 4 } , A 3 = { 1 , 3 , 5 , 7 , 9 } , A 4 = { 5 , 6 , 7 , 8 , 9 } , A 5 = { 0 , 1 , 8 , 9 } . (b) Write down the number of edges in the graph constructed in (a). (c) Write down the degree of each vertex and the sum of the degrees of the vertices in the graph constructed in (a). 3. Seven towns
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/16/2011 for the course CS cs102 taught by Professor Rsharma during the Spring '11 term at IIT Kanpur.

Page1 / 2

102ps1_07 - DEPARTMENT OF MATHEMATICS 102 FINITE...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online