Malaysian Journal of Mathematical Sciences, September 2024, Vol. 18, No. 3
On the Non-Commuting Graph of the Group $U_{6n}$
Khasraw, S. M. S., Abdulla, C., Sarmin, N. H., and Gambo, I.
Corresponding Email: [email protected]
Received date: 24 December 2023
Accepted date: 27 March 2024
Abstract:
Let $G$ be a finite group. The non-commuting graph of $G$ is a simple graph $\Gamma (G)$ whose vertices are elements of $G\backslash Z(G)$, where $Z(G)$ is the center of $G$, and two distinct vertices $a$ and $b$ are joint by an edge if $ab\neq ba$. In this paper, we study the non-commuting graph of the group $U_{6n}$. The independent number, clique and chromatic numbers of the non-commuting graph of the group $U_{6n}$, $\Gamma(U_{6n})$, are determined. Additionally, the resolving polynomial, total eccentricity and independent polynomials of $\Gamma(U_{6n})$ are computed. Finally, the detour and eccentric connectivity indices of $\Gamma(U_{6n})$ are found.
Keywords: non-commuting graph; independent number; chromatic number; clique number; resolving polynomial of a graph
