Square graceful labelings of some subdivision graphs

A graph is said to be a square graceful graph if there exists an injection such that the induced mapping by is a bijection. The function f is called a square graceful labeling of G. In this paper, we prove the graph obtained by the subdivision of the edges of stars of bistar , the graph obtained by the subdivision of the edges of bistar , the graph obtained by the subdivision of the edges of the path in a comb , , and are square graceful graph. ) , ( qp) , (EVG} ,..., 3,2,1,0{) ( : 2 q G V f  } ,..., 9,4,1{) ( : 2 q G E f p  | ) () (| ) (vf uf uvf p   n m B , n m B , n P 1 K P n   n K C , 13 *   m S n :   n K C , 13