Answer to Question #259758 in Discrete Mathematics for rtf

Question

Draw a graph having the given properties

(a) Four vertices each of degree 1

(b) Six vertices each of degree 3 

Answer 1

Method 1

(a) The sum of the numbers of edges that goes in or goes out the vertical is called degree of the vertical

(b) The graph above has all of the required properties:

Verticles 1, 2, 3, 4 has degree one

Verticles 5, 6, 7, 8, 9, 10 has degree three

Method 2.

Four vertices {vA,vB,vC,vD} with two edges {eA, eB} form a graph of 4 vertices of degree 1 each.

Six vertices {v1,v2,v3,v4,v5,v6} with nine edges {e1,e2,e3,e4,e5,e6,e7,e8,e9} form a graph of 6 vertices of degree 3 each.