some algebraic properties of the subdivision graph of a graph

Let g=(v,e) be a connected graph with the vertex-set v and  the edge-set e.  the subdivision graph s(g) of the graph g is obtained from g by adding a vertex in the middle of every edge of g.  in this paper, we investigate some properties of the graphs  s(g) and l(s(g)), where l(s(g)) is the line graph of s(g). we will see that s(g) and  l(s(g))  inherit some  properties of g .    for instance, we show that if g=c_n, then aut(g) = aut(l(s(g))) (as abstract groups), where c_n is the cycle of order n.