Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 9 3 2024 09 01 PI Index of Bicyclic Graphs 425 436 14514 10.22049/cco.2023.27817.1360 EN Manju SC Department of Mathematics, School of Physical Sciences, Kochi, Amrita Vishwa Vidyapeetham, India Somasundaram K Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India Journal Article 2022 05 17 The PI index of a graph $G$ is given by $PI(G)=\sum_{e\in E(G)}(\left|V(G)\right|-N_G(e))$, where $N_G(e)$ is  the number of equidistant vertices for the edge $e$. Various topological indices of bicyclic graphs have already been calculated. In this paper, we obtained the exact value of the PI index of bicyclic graphs. We also explore the extremal graphs among all bicyclic graphs with respect to the PI index. Furthermore, we calculate the PI index of a cactus graph and determine the extremal values of the PI index among cactus graphs. https://comb-opt.azaruniv.ac.ir/article_14514_16693d8f0f62ff339f2efb5cc772d1df.pdf