### Square graceful graphs

#### Abstract

A ( p, q) graph G(V, E) is said to be a square graceful graph if there exists an injection f :V(G)---{0,1,2,3,..., q2 } such that the induced mapping f p : E(G) --- {1, 4, 9,..., q2} defined by f (uv)=| f (u) f (v)| p = ? is a bijection.

The function f is called a square labeling of G . In this paper, we prove that the star n K 1, , bistar m n B , , the graph obtained by the subdivision of the edges of the star K1,n , the graph obtained by the subdivision of the central edge of the bistar Bm,n , the generalised crown n C K 3 1, ? , graph 1 P nK m ? (n ? 2) , the comb 1 P K n? , graph ( , ) m n P S , (3, t) kite graph (t ? 2) and the path Pn are square graceful graphs.

#### References

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