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**1 - 1**of**1**### Square and Cube Difference Labeling of Cycle Cactus, Special Tree and a New Key Graphs

, 2014

"... Let G be a (p, q) graph. G is said to be a square difference labeling if there exists a injection f: V(G) → {0,1,2,…,n-1} such that the edge set of G has assigned a weight defined by the absolute square difference of its end-vertices, the resulting weights are distinct. A graph which admits square ..."

Abstract
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Let G be a (p, q) graph. G is said to be a square difference labeling if there exists a injection f: V(G) → {0,1,2,…,n-1} such that the edge set of G has assigned a weight defined by the absolute square difference of its end-vertices, the resulting weights are distinct. A graph which admits square difference labeling is called square difference graph. Shiama has obtained square difference labeling for some graphs like path, cycle, star (K1,n-1), fan, crown (Cn⨀K1). Let G be a (p, q) graph. G is said to be a cube difference labeling if there exists a injection f: V(G) → {0, 1, 2, …, n-1} such that the edge set of G has assigned a weight defined by the absolute cube difference of its end-vertices, the resulting weights are distinct. A graph which admits cube difference labeling is called cube difference graph. We have proved the square and cube difference labeling for graphs like cycle cactus graph Ck(3) and the tree <K1,n: 2> and a newly defined key graph in this paper.