A note on the coprime graph of a group

Dorbidi, Hamid Reza

doi:10.22108/ijgt.2016.9125

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	A note on the coprime graph of a group
International Journal of Group Theory
مقاله 30، دوره 5، شماره 4، اسفند 2016، صفحه 17-22 اصل مقاله (196.33 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2016.9125
نویسنده
Hamid Reza Dorbidi^*
Department of Basic Sciences, University of Jiroft, Jiroft, Kerman, Iran
چکیده
‎In this paper we study the coprime graph of a group $G$‎. ‎The‎ ‎coprime graph of a group $G$‎, ‎denoted by $\Gamma_G$‎, ‎is a graph‎ ‎whose vertices are elements of $G$ and two distinct vertices $x$‎ ‎and $y$ are adjacent if and only if $(\|x\|,\|y\|)=1$‎. ‎In this paper‎, ‎we ‎show that $\chi(\Gamma_G)=\omega(\Gamma_G).$ We classify all the‎ ‎groups which $\Gamma_G$ is a complete $r-$partite graph or a‎ ‎planar graph‎. ‎Also we study the automorphism group of‎ ‎$\Gamma_G$‎.
کلیدواژه‌ها
coprime graph؛ Planner graph؛ automorphism group

مراجع
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A note on the coprime graph of a group