TY  - JOUR
T1  - THE SZEGED INDEX OF POWER GRAPH OF FINITE GROUPS
AU  - Banerjee, Subarsha
PY  - 2025
DA  - September
Y2  - 2024
JF  - TWMS Journal of Applied and Engineering Mathematics
JO  - JAEM
PB  - Işık University Press
WT  - DergiPark
SN  - 2146-1147
SP  - 2166
EP  - 2180
VL  - 15
IS  - 9
LA  - en
AB  - The Szeged index of a graph is an invariant with several applications in chemistry. The power graph of a finite group $G$ is a graph having vertex set as $G$ in which two vertices $u$ and $v$ are adjacent if  $v=u^m$ or $u=v^n$ for some $m,n\in \mathbb{N}$. In this paper, we first obtain a formula for the Szeged index of the generalized join of graphs. As an application, we obtain the Szeged index of the power graph of the finite cyclic group $\mathbb Z_n$ for any $n>2$. We further obtain a relation between the Szeged index of the power graph of $\mathbb Z_n$ and the  Szeged index of the power graph of the dihedral group $\mathrm{D}_n$. We also provide SAGE codes for evaluating the Szeged index of the power graph of $\mathbb{Z}_n$ and $\mathrm{D}_n$ at the end of this paper.
KW  - Szeged index
KW  - generalized join
KW  - power graph
KW  - finite cyclic group
KW  - dihedral group
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UR  - https://dergipark.org.tr/en/pub/twmsjaem/article/1792003
L1  - https://dergipark.org.tr/en/download/article-file/5278304
ER  -