TY - JOUR
ID - 113913
TI - On Power Graph of Some Finite Rings
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Soleimani, Masoumeh
AU - Naderi, Mohamad Hasan
AD - Department of Mathematics, Faculty of Science, University of Qom, Qom, I. R. Iran
Y1 - 2023
PY - 2023
VL - 8
IS - 2
SP - 161
EP - 173
KW - Domination number
KW - Independence number
KW - Split graph
KW - Unit Semi-cartesian product
DO - 10.22052/mir.2020.185443.1132
N2 - Consider a ring $R$ with order $p$ or $p^2$, and let $\mathcal{P}(R)$ represent its multiplicative power graph. For two distinct rings $R_1$ and $R_2$ that possess identity element 1, we define a new structure called the unit semi-cartesian product of their multiplicative power graphs. This combined structure, denoted as $G.H$, is constructed by taking the Cartesian product of the vertex sets $V(G) \times V(H)$, where $G = \mathcal{P}(R1)$ and $H = \mathcal{P}(R2)$. The edges in $G.H$ are formed based on specific conditions: for vertices $(g,h)$ and $(g^\prime,h^\prime)$, an edge exists between them if $g = g^\prime$, $g$ is a vertex in $G$, and the product $hh^\prime$ forms a vertex in $H$.
Our exploration focuses on understanding the characteristics of the multiplicative power graph resulting from the unit semi-cartesian product $\mathcal{P}(R1).\mathcal{P}(R2)$, where $R_1$ and $R_2$ represent distinct rings. Additionally, we offer insights into the properties of the multiplicative power graphs inherent in rings of order $p$ or $p^2$.
UR - https://mir.kashanu.ac.ir/article_113913.html
L1 - https://mir.kashanu.ac.ir/article_113913_bf42aa77937e1397e8c14b8b39bac3e3.pdf
ER -