PI Index of Bicyclic Graphs

Document Type : Original paper


1 Mathematics, Amrita Vishwa Vidyapeetham, Kochi, India

2 Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India.


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.


Main Subjects

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