For a nite group G, the mobius function graph M(G) is the simple graph whose vertices are elements of the group G with adjacency dened between vertices a and b if and only if (jaj jbj)=(jaj)(jbj). Topological indices and laplacian spectrum with their applications in molecular chem- istry is an acute topic of research in Mathematics. This paper analyses some basic properties of mobius function graph of dihedral groups M(D2n) and discusses topological indices, such as rst and second Zagreb index, Wiener and hyper - Wiener index and nally Harary index along with the laplacian spectrum of M(D2n).