ISRO2018-38

Question

The number of edges in a regular graph of degree: $d$ and $n$ vertices is:

• A. maximum of $n$ and $d$ 
• B. $n +d$
• C. $nd$
• D. $nd/2$

Answer 1

as every vertex has degree d,so sum of degrees is n*d.

we know 2* number of edges = sum of degrees

          so,2*E = nd

              =>E=$\frac{nd}{2}$

Answer 2

Regular graph, a graph in which all vertices have same degree.

example:- if n=3 and d=2 so there are 3*2/2 = 3 edges.
                 if n=4 and d=2 so there are 4*2/2 = 4 edges. and so on.

So option D is correct.

Answer 3

Every complete graph with n vertices(K_n) is a regular graph of degree 'n-1' therefore 

no. of edges in K_n=n(n-1)/2

                            =n(d)/2

                           = ( n * d ) / 2