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A simple graph  is said to be an -covering if every edge of  belongs to at least one subgraph isomorphic to . A bijection  is an (a,d)--antimagic total labeling of  if, for all subgraphs  isomorphic to , the sum of labels of all vertices and edges in  form an arithmetic sequence  where , are two fixed integers and  is the number of all subgraphs of  isomorphic to . The labeling  is called super if the smallest possible labels appear on the vertices. A graph that admits (super) --antimagic total labeling is called (super) --antimagic. For a special , the (super) --antimagic total labeling is called -(super)magic labeling. A graph that admits such a labeling is called -(super)magic. The -shadow of graph ,, is a graph obtained by taking  copies of , namely, , and then joining every vertex  in ,, to the neighbors of the corresponding vertex  in . In this paper we studied the -supermagic labelings of  where  are paths and cycles.

international journal of mathematics and mathematical sciences

On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:math>-Supermagic Labelings of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:math>-Shadow of Paths and Cycles

On H-Supermagic Labelings of m-Shadow of Paths and Cycles