Laplacian spectrum characterization of extensions of vertices of wheel graphs and multi-fan graphs

AbstractThe graph Cn1∇Kk is the product of a circuit Cn1 and a clique Kk. In this paper, we will prove that it is determined by their Laplacian spectrum except when n1=6. If n1=6, there are several counterexamples. We also prove that the product of s vertex–disjoint paths and a clique (Pn1∪Pn2∪⋯∪Pns)∇Kk is also determined by the Laplacian spectrum