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 edgeset 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 Cn, then Aut(G) = Aut(L(S(G))) (as abstract groups), where Cn is the cycle of order n. [ABSTRACT FROM AUTHOR]