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A non-commuting graph of a finite group $G$ is a graph whose vertices arenon-central elements of $G$ and two vertices are adjacent if they don't commutein $G$. In this paper, we study the non-commuting graph of the group $U_{6n}$and explore some of its properties including the independent number, clique andchromatic numbers. Also, the general formula of the resolving polynomial of thenon-commuting graph of the group $U_{6n}$ are provided. Furthermore, we findthe detour index, eccentric connectivity, total eccentricity and independentpolynomials of the graph.

On the Non-Commuting Graph of the Group $U_{6n}$