A note on the stability results of the number of cliques in graphs with given matching number

Duan, Ning, Peng, Wang and Yang determined the maximum number of s-cliques of a graph with given minimum degree and matching number. In this note, we prove a stability version of their theorem. Namely, we prove that if the number of s-cliques in a graph G is close to the above maximum number from their theorem, then G must be a subgraph of some well-specified graphs.