im really confused on this Either draw a graph with the spec

im really confused on this

Either draw a graph with the specified properties or explain why no such graph exists: (a) A graph with four vertices of degree {1,1,1,4}. (b) A simple graph with five vertices of degree {2,3,3,3,5}. (c) A simple graph with nine edges and all vertices of degree 3.

Solution

(a) Asimple graph with 4 vertices of degree 1,1,1,4 is not possible . because there are 4 vertices and if graph is made maximum of 2 one degee graph is made and other 2 vertices should be greater than 1 degree.

(b) A simple graph with five vertices with degrees 2, 3, 3, 3, and 5. It is impossible to draw this graph. A simple graph has no parallel edges nor any loops. There are only 5 vertices, so each vertex can only be joined to at most four other vertices, so the maximum degree of any vertex would be 4. Hence, you can’t have a vertex of degree 5.