Square Graceful Labeling of Some Graphs
نویسنده
چکیده
A p. q graph G = V,E is said to be a square graceful graph ifthere exists an injective function f: V G → 0,1,2,3,... , q such that the induced mapping fp : E G → 1,4,9,... , q 2 defined by fp uv = f u − f v is an injection. The function f is called a square graceful labeling of G. In this paper the square graceful labeling of the caterpillar S X1,X2 ,... ,Xn , the graphs Pn−1 1,2,...n ,mK1,n ∪ sK1,t , K1,i , n i=1 Pn⨀K1 − e,H graph and some other graphsare studied. A new parameter called star square graceful deficiency number of a graph is defined and the star square graceful deficiency number of the cycle C3 is determined. Two new definitions namely, odd square graceful labeling and even square graceful labeling of a graph are defined with example.
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