bounds of the symmetric division deg index for trees and unicyclic graphs with a perfect matching

The symmetric division deg index is a well-established valuable index in the analysis of quantitative structure-property and structure-activity relationships for molecular graphs. in this paper, we study the range of sdd index for special classes of trees and unicyclic graphs. we present the first four lower bounds for sdd index of trees and unicyclic graphs, which admit a perfect matching and find the subclasses of graphs that attain these bounds. further, we also compute the upper bounds of sdd index for the collection of molecular graphs, namely the trees and unicyclic graphs, each having maximum degree four and that admit a perfect matching.