Signless-Laplacian determination conjecture for multicone cycle graphs

Let $K_w$ be the complete graph on $w$ vertices, let $C_n$ be the cycle graph on $n$ vertices, and let $mC_n$ denote the disjoint union of $m$ copies of $C_n$. Write $G\bigtriangledown H$ for the join of graphs $G$ and $H$. A graph is DS with respect to its signless Laplacian spectrum if every graph with the same signless Laplacian spectrum is isomorphic to it. Signless-Laplacian multicone conjecture. The multicone graphs $K_w\bigtriangledown mC_n$ are DS with respect to their signless Laplacian spectra. The paper proves adjacency- and Laplacian-spectral determination for connected multicone graphs of this form, but leaves the signless-Laplacian assertion as a conjecture.