Augmented Zagreb index of trees and unicyclic graphs with perfect matchings

Abstract The augmented Zagreb index of a graph G , which is proven to be a valuable predictive index in the study of the heat of formation of octanes and heptanes, is defined as A Z I ( G ) = ∑ u v ∈ E ( G ) ( d ( u ) d ( v ) d ( u ) + d ( v ) − 2 ) 3 , where E ( G ) is the edge set of G, d ( u ) and d ( v ) are the degrees of the terminal vertices u and v of edge uv . In this paper, the lower bounds on augmented Zagreb index of trees and unicyclic graphs with perfect matchings are presented, and the corresponding extremal trees and uinicyclic graphs with perfect matchings are characterized.