2 Does there exist i a graph ii a simple graph with the foll

2. Does there exist (i) a graph, (ii) a simple graph with the following degree sequence? If so, draw a picture of such a graph. If not, explain why.

(a) (2,2,2,3,3,5,5)

(b) (1,1,3,3,5,5,5)

(c) (0,2,2,2,3,5,6)

Solution

a) given (2,2,2,3,3,5,5)

number of vertices=7

Degree of all vertices is less than or equal to n ( no.of vertices)

Odd number vertices are four.

There is no degree less than zero

Remove 2