Maximizing the number of independent sets of fixed size in Kn‐covered graphs

For some given graph H, a G is called H-covered if each vertex in contained copy of H. In this note, we determine the maximum number independent sets size t ≥ 3 N-vertex K n -covered graphs and classify extremal graphs. The result answers question proposed by Chakraborti Loh. proof uses an edge-switching operation on hypergraphs which never increases sets.