Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination

Abstract

Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M₁ and the second Zagreb index M₂ have already studied. In particular, it has been presented, the first Zagreb index M₁ and the second Zagreb index M₂ of trees T in terms of domination parameter. In this paper, we present upper bounds on Zagreb indices of unicyclic and bicyclic graphs with a given domination number and also find upper bounds on the Zagreb indices of trees, unicyclic, and bicyclic graphs with a given total domination number.