Some extremal graphs with respect to inverse degree

The inverse degree of graph GG is defined as ID(G)=∑v∈V(G)1dG(v) where dG(v)dG(v) is the degree of vertex vv in GG. In this paper we have determined some upper and lower bounds on the inverse degree ID(G)ID(G) for a connected graph GG in terms of other graph parameters, such as chromatic number, clique number, connectivity, number of cut edges, matching number. Also the corresponding extremal graphs have been completely characterized.