Bounds of the Symmetric Division Deg Index for Trees and Unicyclic Graphs with a Perfect Matching

Document Type : Research Paper


Department of Mathematical Sciences, IIT (BHU) Varanasi


The Symmetric division deg (SDD) 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.


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