A Unified Approach to the Extremal Zagreb Indices for Trees, Unicyclic Graphs and Bicyclic Graphs 1

Abstract

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. This paper presents a unified and simple approach to the largest and smallest Zagreb indices for trees, unicyclic graphs and bicyclic graphs by introducing some transformations, and characterize these graphs with the largest and smallest Zagreb indices, respectively.