When is complete bipartite graph regular..?

Question

Complete bipartite graph Km,n is regular when 

a) m= 1

b) n=1

c) both a) and b)

d) none

Answer is c....but whenever m=n , complete bipartite graph is regular.

So why there is a condition of m=n=1.....?????

Plz explain........................

Answer 1

It is used for this question only actually whenever m=n the complete bipartite graph is regular. here they want to just test the concept whether we know this or not and how patiently we go through all options.

Answer 2

Regular Graph = Every graph has same no of edges incident / Degree of each vertex is same

Complete Bipartite graph  Km,n is regular if & only if m = n.

So

A) & B) are both false.

Counter example for A) K 2,1

B) K 1,2

As A & B are false c) both a) and b) must be false. (Even you take both option together m = 1 & n =1 don't give you set of all Km,m regular graphs)

D) Is correct. When m = n , complete Bipartite graph is regular & It can be called as m regular graph.

Answer 3

(C) option .correct 
 regular graph means all vertices  having same degree .. here they talk about complete bipartitie graph

suppose take K_1,1  in this graph we have only one edge between two vertices .

if we take K_2,3  means this bipartite graph has two set of vertices partition one partition contain two vertices and second partition contain three vertices .when u make this graph as complete bipartite graph than degree of the vertices are not same untill u dont take M=N=1. ie K_m,n  (where m=n)

Comments

M = N is okay .

M = N = 1 is not !

You are omitting all other graphs !