Study of Bounds and Extremal Graphs of Symmetric Division Degree Index for Bicyclic Graphs with Perfect Matching

Abstract

In this article, we complement the study of Pan and Li by computing the first five minimum values of the symmetric division degree (SDD) index attained by bicyclic graphs that have a perfect matching. One of our main contributions is identifying the graphs that attain the bounds. Further, we compute the upper bound of the SDD index for bicyclic graphs with a maximum degree of four, which admits a perfect matching and prove the bound is also tight by identifying the graphs that attain it. © 2022. University of Kashan Press. All rights reserved