Graphs with six distinct matching roots

• Graphs with eigenvalues, Signless Laplacian eigenvalues have structural properties.
• There is a close connection between the spectral properties & matching polynomial.
• We characterize the graphs which only have six distinct matching roots.
• It has some new information of matching polynomial of graphs.

We investigate graphs whose matching polynomial has six distinct roots. We show that for those graphs if its order n>6n>6 then they are determined by their matching polynomials.