GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
116 views

Find the matching number for the given graph-

asked in Graph Theory by Active (1.2k points)   | 116 views

2 Answers

+4 votes
Matching  it means that no 2 edges are adjacent simply a vertex with degree 1

if we have a vertex with degree 0 we say not matched

In the above graph if we start with G we have 2 edges for G In matching we consider 1 edge since if both are considered we get degree of G as 2 so if we consider G-A edge then node 2 is alone and has degree 0 it makes graph to be not matched so we consider G-2 edge , A-0 edge  T has edges with 0 and 1 since A-0 edge is present if we consider 0 then degree of 0 is 2 so we don't consider

we have T-1 edge then we are left with edge E-6

Totally we get (G-2),(A-0),(T-1),(E-6) so matching number is 4
answered by Veteran (13.5k points)  
0 votes

The matching number nu(G) of graph G, sometimes known as the edge independence number, is the size of a maximum independent edge set.

and maximum means max beween the minimal independence edge sets,which we can form from the graph.So here  

maximum independent edge set is { (G,2) , (A,0) , (T,1) , (E,6) } hence ans is 4.

 

answered by Boss (6.5k points)  

Related questions

+1 vote
1 answer
1
asked in Graph Theory by shikharV Boss (5.1k points)   | 149 views
0 votes
1 answer
3
Top Users Jan 2017
  1. Debashish Deka

    8608 Points

  2. sudsho

    5398 Points

  3. Habibkhan

    4718 Points

  4. Bikram

    4522 Points

  5. Vijay Thakur

    4468 Points

  6. saurabh rai

    4222 Points

  7. Arjun

    4122 Points

  8. santhoshdevulapally

    3742 Points

  9. Sushant Gokhale

    3576 Points

  10. GateSet

    3394 Points

Monthly Topper: Rs. 500 gift card

19,177 questions
24,073 answers
52,975 comments
20,310 users