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