Spectral extremal graphs for disjoint cliques (Q2684892)

In this paper, the authors consider the graph \(G\) which has the maximum spectral radius among all graphs without \(k\) disjoint cliques, and show that if \(G\) attains the maximum spectral radius over all \(n\)-vertex \(kK_{r+1}\)-free graphs for sufficiently large \(n\), then \(G\) is isomorphic to the join of a complete graph \(K_{k-1}\) and an \(r\)-partite Turán graph \(T_{n-k+1,r}\).