Summary: This paper presents the recurrence relation using to count a number of perfect matchings in linear chain and snake chain graphs. These graphs are offen found in the chemical structure. A perfect matching graph \(M\) is a subgraph of \(G\) where there are no edges in \(M\) adjacent to each other and \(V(M)=V(G)\). \(\phi(G)\) is a number of perfect matching of \(G\) which leads to important chemical properties.
The results show that a number of perfect matching of a linear chain graph depends on parity of faces and number of edges in each face. A number of perfect matching of a snake chain graph depends on parity of the chain.