A note on the order graph of a group

Document Type : Research Paper

Author

University of Jiroft

Abstract

 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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References

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[5] Sh. Payrovi, H. Pasebani, The Order Graphs of Groups, J Algebraic Structures and Their Applications, 1
(no 1) ( 2014 ), 1-10.
[6] J. S. Wiliams, Prime Graph Components of Finite Groups, J. Algebra 69 (1981), 487-513.
Algebraic Structures and Their Applications
Volume 3, Issue 1
February 2016
Pages 17-24

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