Super antimagic total labeling under duplication operations

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0062

Keywords:

Super edge-antimagic total graph, Super vertex-antimagic total graph, Duplication operations, Prism, Antiprism, Crossed prism, Cycle and complete graphs

Abstract

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.

Author Biographies

Abdul Jalil M. Khalaf, University of Kufa.

Dept. of Mathematics.

Muhammad Naeem, Institute of Southern Punjab.

Dept. of Mathematics and Statistics.

Muhammad Kamran Siddiqui, COMSATS University Islamabad.

Dept. of Mathematics.

Abdul Qudair Baig, Institute of Southern Punjab.

Dept. of Mathematics and Statistics.

References

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Published

2020-07-28

How to Cite

[1]
A. J. M. Khalaf, M. Naeem, M. K. Siddiqui, and A. Q. Baig, “Super antimagic total labeling under duplication operations”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 995-1003, Jul. 2020.