Some new results on non-inverse graph of a group

The non-inverse graph corresponding to a group G, is a simple graph with vertices being elements of the group G and there is an edge between two vertices if they are not mutual inverses. In the current paper, we study few properties of the non-inverse graphs of groups. We also discuss the parameters related different types of domination no.s of the non-inverse graph. We further obtain the Laplacian spectra and signless Laplacian spectra of the non-inverse graphs.