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PI Index of Bicyclic Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 9، شماره 3، آذر 2024، صفحه 425-436 اصل مقاله (418.88 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.27817.1360 | ||
| نویسندگان | ||
| Manju SC* 1؛ Somasundaram K2 | ||
| 1Department of Mathematics, School of Physical Sciences, Kochi, Amrita Vishwa Vidyapeetham, India | ||
| 2Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| PI index؛ Unicyclic graphs؛ Bicyclic graphs؛ Extremal values | ||
| مراجع | ||
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