TY - JOUR
ID - 14514
TI - PI Index of Bicyclic Graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - SC, Manju
AU - K, Somasundaram
AD - Department of Mathematics, School of Physical Sciences, Kochi,
Amrita Vishwa Vidyapeetham, India
AD - Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India
Y1 - 2024
PY - 2024
VL - 9
IS - 3
SP - 425
EP - 436
KW - PI index
KW - Unicyclic graphs
KW - bicyclic graphs
KW - Extremal values
DO - 10.22049/cco.2023.27817.1360
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14514.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14514_16693d8f0f62ff339f2efb5cc772d1df.pdf
ER -