Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21289320240901PI Index of Bicyclic Graphs4254361451410.22049/cco.2023.27817.1360ENManjuSCDepartment of Mathematics, School of Physical Sciences, Kochi,
Amrita Vishwa Vidyapeetham, IndiaSomasundaramKDepartment of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India0000-0003-2226-1845Journal Article20220517The 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.http://comb-opt.azaruniv.ac.ir/article_14514_16693d8f0f62ff339f2efb5cc772d1df.pdf