TY - JOUR
AU - Khuhirun, Borworn
AU - Jantarakhajorn, Khajee
AU - Maneerut, Wanida
PY - 2023/12/31
Y2 - 2024/06/24
TI - On the Connectivity of Non-Commuting Graph of Finite Rings: Discrete and Computational Geometry, Graphs, and Games
JF - Thai Journal of Mathematics
JA - Thai J Math
VL - 21
IS - 4
SE - Articles
DO -
UR - https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1554
SP - 887–898
AB - <p>The non-commuting graph of a non-commutative ring $R$, denoted by $\Gamma_{R}$, is a simple graph with vertex set of elements in $R$ except for its center. Two distinct vertices $x$ and $y$ are adjacent if $xy
eq yx$. In this paper, we study the vertex-connectivity and edge-connectivity of a non-commuting graph associated with a finite non-commutative ring $R$ and prove their lower bounds. We show that the edge-connectivity of $\Gamma_{R}$ is equal to its minimum degree. The vertex-connectivity and edge-connectivity of $\Gamma_{R}$ are determined when $R$ is a non-commutative ring of order $p^{n}$ where $p$ is a prime number, and $n \in \left\{2,3,4,5\right\}$.</p>
ER -