Let  be a simple graph of order n and size m with maximum degree D and minimum degree d and with no isolated vertices. The inverse index of G is defined as

where  is the degree of the vertex  In this paper, we obtain lower and upper bounds on  of graph G and characterize graphs for which these bounds are best possible. Moreover, we compare inverse index  with the topological index  We also study the inverse index from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices.

inverse index, topological index, spectra of graphs, regular graphs.