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On - Supermagic Labelings of - Shadow of Paths and Cycles

Author

Listed:
  • Ika Hesti Agustin
  • F. Susanto
  • Dafik
  • R. M. Prihandini
  • R. Alfarisi
  • I. W. Sudarsana

Abstract

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.

Suggested Citation

  • Ika Hesti Agustin & F. Susanto & Dafik & R. M. Prihandini & R. Alfarisi & I. W. Sudarsana, 2019. "On - Supermagic Labelings of - Shadow of Paths and Cycles," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-7, February.
    • Handle: RePEc:hin:jijmms:8780329
    DOI: 10.1155/2019/8780329
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