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Square Graceful Labeling of Some Graphs

K.Murugan

A ð�?. ð�?�? graph G = ð�?�?, 𝐸 is said to be a square graceful graph ifthere exists an injective function f: V 𝐺 → 0,1,2,3, … , ð�?�?2 such that the induced mapping ð�?�?ð�? : E 𝐺 → 1,4,9, … , ð�?�?2 defined by ð�?�?ð�? ð�?¢ð�?£ = ð�?�? ð�?¢ − ð�?�? ð�?£ 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 ð�?�?1, ð�?�?2, … , ð�?�?ð�?�? , the graphs ð�?�?ð�?�? −1 1,2, … ð�?�? ,m𝐾1,ð�?�? ∪ ð�? ð¾1,ð�?¡ , 𝐾1,ð�?�? , ð�?�?ð�?�? =1 ð�?�?ð�?�? â¨�?𝐾1 − ð�?�?,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.