Parameters of the coprime graph of a group
Publish place: International Journal of Group Theory، Vol: 10، Issue: 3
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_THEGR-10-3_004
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
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 $(o(g),o(h))=۱$. 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.
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Authors
Jessie Hamm
Department of Mathematics, Winthrop University, ۱۴۲ Bancroft Hall Rock Hill, SC, USA
Alan Way
Department of Mathematics, Winthrop University, ۱۴۲ Bancroft Hall Rock Hill, SC, USA