A note on the order graph of a group

Document Type : Research Paper


University of Jiroft


 The order graph of a group $G$, denoted by $\Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|\big{|}|K|$ or $|K|\big{|}|H|$.
 In this paper, we study the connectivity and diameter of this  graph. Also we give a relation between the order graph and prime  graph of a group.


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