University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 13 2 2022 06 01 Study of Bounds and Extremal Graphs of Symmetric Division Degree Index for Bicyclic Graphs with Perfect Matching 145 165 112052 10.22052/ijmc.2022.243396.1605 EN Abhay Rajpoot Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh-221005, INDIA Lavanya Selvaganesh Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh-221005, INDIA Journal Article 2022 01 05 In this article, we complement the study of Pan and Li by computing the first five minimum values of the symmetric division degree (<em>SDD</em>) 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 <em>SDD</em> 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. https://ijmc.kashanu.ac.ir/article_112052_cba8cca77a941af620e8337dd759b593.pdf