+1 vote
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Given explanation:

In the above explanation, it is written that matching number is 4 but I am getting matching number as 3 for this graph(choosing edges 1-2, 3-4 and 6-7). Please check where I am going wrong

You are calculating edge covering number.

Matching number : 4 (1-2,3-4,5-6,8-7)
Thanks!
I think edge cover is also 4.. 1-2 3-4 6-7 is not covering verter #8..
matching number-4

it can also be

(3-4)(2-5)(1-6)(8-7)

+1 vote

In Matching graph no 2 edges are adjacent it means the degree of vertex is 1

So we find such vertices and edges

Let us start with 2 then we get (2-1),(3-8),(4-7),(5-6) these edges are matching so the matched number is  4

Even these edges (2-3),(1-8),(4-5),(7-6) are matching so the matched number is  4

These edges (2-5),(3-4),(1-6),(8-7) are matching so the matched number is  4

By choosing these edges we could have vertices with 1 degree

option a is true matching number is 4 ,( 12 , 38, 47,56)

option b is also true  because it is bipartite graph .

option c is true as matching covers every vertex.

option d is not true . It is not complete bipartite.