Discrete mathematics Class MAD 1100 Chapter 8 Graph Theory 9

9. Give an example of a graph with degree sequence 3,2,1,0, or show that such a graph cannot exist.

Solution

Given that there are 4 vertices in a graph and degree one of the vertex is 3.

Therefore one vertex must adjacent with every other vertex of the graph.

Hence degree of every vertex is non zero.

But given that there is vertex with degree 0.

Hence this type of graph does not exists.