Some extremal graphs with respect to inverse degree.

The inverse degree of graph G is defined as I D ( G ) = ∑ v ∈ V ( G ) 1 d G ( v ) where d G ( v ) is the degree of vertex v in G . In this paper we have determined some upper and lower bounds on the inverse degree I D ( G ) for a connected graph G 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. [ABSTRACT FROM AUTHOR]