Super antimagic total labeling under duplication operations

• Khalaf, Abdul Jalil M. ^[1] ; Naeem, Muhammad ^[3] ; Siddiqui, Muhammad Kamran ^[2] ; Baig, Abdul Qudair ^[3]
  1. [1] University of Kufa

     University of Kufa

     Irak

     
  2. [2] COMSATS Institute of Information Technology

     COMSATS Institute of Information Technology

     Pakistán

     
  3. [3] Institute of Southern Punjab.

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. Extra 4, 2020 (Ejemplar dedicado a: Special Issue: Mathematical Computation in Combinatorics and Graph Theory; i), págs. 995-1003
• Idioma: inglés
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• Resumen

  • For a graph G the duplication operation of a vertex v by a new edge e = uw results in a new graph G’ such that N (u) = {v, w} and N (w) = {v, u}. The duplication operation of an edge e = uv by a new vertex w results in a new graph G’’ such that N (w) = {u, v}. In this article we have discussed that the properties of a graph, with minimum degree 2 of any vertex, to be super vertex-antimagic total and to be super edge-antimagic total are invariant under the above duplication operations. Also, we have discussed on the existence of the so-called k super vertex-antimagic total vertex modifications and k super edge-antimagic total edge modifications for graphs.