hi Harikesh, we take a example W4(wheel-4) for matching.
we first make a set of edges ,
i.e. E = {{p,q},{p,r},{p,t},{r,t},{r,s},{s,q},{s,t},{q,t}}
according to definition of MATCHING: we make a subset of set E such that no two edges are incident on same vertex.
so, here there will be 10 MATCHINGS of this graph.
MATCHING:1 {{p,q},{r,s}}
MATCHING:2 {{p,r},{s,q}}
MATCHING:3 {{p,t},{r,s}}
MATCHING:4 {{p,t},{s,q}}
MATCHING:5 {{r,t},{s,q}}
MATCHING:6 {{r,t},{p,q}}
MATCHING:7 {{s,t},{p,q}}
MATCHING:8 {{s,t},{p,r}}
MATCHING:9 {{q,t},{p,r}}
MATCHING:10 {{q,t},{r,s}}