%0 Journal Article
%T The subgroup graph of a group
%A David F. Anderson
%A Jodi Fasteen
%A John D. LaGrange
%J Arabian Journal of Mathematics
%@ 2193-5351
%D 2012
%I 
%R 10.1007/s40065-012-0018-1
%X Given any subgroup H of a group G, let ¦£ H (G) be the directed graph with vertex set G such that x is the initial vertex and y is the terminal vertex of an edge if and only if x ¡Ù y and ${xy\in H}$ . Furthermore, if ${xy\in H}$ and ${yx\in H}$ for some ${x,y\in G}$ with x ¡Ù y, then x and y will be regarded as being connected by a single undirected edge. In this paper, the structure of the connected components of ¦£ H (G) is investigated. All possible components are provided in the cases when |H| is either two or three, and the graph ¦£ H (G) is completely classified in the case when H is a normal subgroup of G and G/H is a finite abelian group.
%K 05C25
%K 20B05
%U http://link.springer.com/article/10.1007/s40065-012-0018-1