3,862 views

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........................

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.
by

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.

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

suppose take K1,1  in this graph we have only one edge between two vertices .

if we take K2,3  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 Km,n  (where m=n)

### 1 comment

M = N is okay .

M = N = 1 is not !

You are omitting all other graphs !