Nordhaus-gaddum type relations for some topological indices

Abstract

A Nordhau-Gaddum type relation is the one associated with some parameter of a graph and its complement. Nordhaus-Gaddum type relations have been studied since 1956. The most famous relation is the upper bound for the sum of the chromatic numbers of a graph and its complement. In this work, the Nordhaus-Gaddum type difference relation for the first Zagreb index, the Nordhaus-Gaddum type sum relation with the help of Cangul index, the Nordhaus-Gaddum type sum relation for the second Zagreb index and total irregularity index are studied. Further, Nordhaus-Gaddum type relations for omega invariant are also found out.