Generalized order divisor graphs of finite group
نویسندگان
1 Scientific Analysis Group, Defence Research and Development Organisation, Metcalfe House, Delhi, India
2 Mathematics, Assistant Professor, S.S. Govt. P.G. College, Tigaon, Faridabad, Haryana, India
3 Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, India
4 Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, India
doi
10.22108/ijgt.2022.133091.1787چکیده
Let $G$ be a finite group and $k$ a fixed positive integer. We define the generalized order divisor graph of $G$ to be a graph whose vertex set is the group $G$ and in which two vertices $a$ and $b$ are adjacent if and only if the orders $o(a^k)$ and $o(b^k)$ are different and either $o(a^k)$ divides $o(b^k)$ or $o(b^k)$ divides $o(a^k)$. This generalizes the order divisor graphs of finite groups. Some properties of our graph are introduced, and we investigate the structure of the generalized order divisor graphs of finite cyclic groups.
