There are many different graphs one can associate to a group. Some examples are the well-known Cayley graph, the zero divisor graph (of a ring), the power graph, and the recently introduced coprime graph of a group. The coprime graph of a group $G$, denoted $\Gamma_G$, is the graph whose vertices are the group elements with $g$ adjacent to $h$ if and only if $(o(g),o(h))=1$. In this paper we calculate the independence number of the coprime graph of the dihedral groups. Additionally, we characterize the groups whose coprime graph is perfect.
Hamm, J., Way, A. (2021). Parameters of the coprime graph of a group. International Journal of Group Theory, 10(3), 137-147. doi: 10.22108/ijgt.2020.112121.1489
MLA
Jessie Hamm; Alan Way. "Parameters of the coprime graph of a group". International Journal of Group Theory, 10, 3, 2021, 137-147. doi: 10.22108/ijgt.2020.112121.1489
HARVARD
Hamm, J., Way, A. (2021). 'Parameters of the coprime graph of a group', International Journal of Group Theory, 10(3), pp. 137-147. doi: 10.22108/ijgt.2020.112121.1489
VANCOUVER
Hamm, J., Way, A. Parameters of the coprime graph of a group. International Journal of Group Theory, 2021; 10(3): 137-147. doi: 10.22108/ijgt.2020.112121.1489
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