Super antimagic total labeling under duplication operations
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-04-0062Keywords:
Super edge-antimagic total graph, Super vertex-antimagic total graph, Duplication operations, Prism, Antiprism, Crossed prism, Cycle and complete graphsAbstract
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.
References
M. Bača, F. Bertault, J. Macdougall, M. Miller, R. Simanjuntak, and Slamin, “Vertex-antimagic total labelings of graphs”, Discussiones mathematicae graph theory, vol. 23, no. 1, p. 67, 2003, doi: 10.7151/dmgt.1186
R. M. Figueroa-Centeno, R. Ichishima, and F. A. Muntaner-Batle, “On super edge-magic graphs”, Ars combinatoria, vol. 64, pp. 81-95, 2002. [On line]. Available: https://bit.ly/2BN4aIy
P. Kovář and J. A. Gallian, “Magic labelings of regular graphs”, AKCE international journal of graphs and combinatorics, vol. 4, no. 3, pp. 261-275, 2007, doi: 10.1080/09728600.2007.12088841
J. Sedláček, “On magic graphs”, Mathematica slovaca, vol. 26, no. 4, pp. 329-335, 1976. [On line]. Available: https://bit.ly/3e9Ygy6
K. A. Sugeng, M. Miller, Y. Lin, and M. Bača, “Super (a,d)-vertex antimagic total labelings”, Journal of combinatorial mathematics and combinatorial computing, vol. 55, pp. 91-102, 2005.
S. K. Vaidya and C. M. Barasara, “Product cordial graphs in the context of some graph operations”, International journal of computing science and mathematics, vol. 1, no. 2, pp. 1-6, 2011. [On line]. Available: https://bit.ly/2DlhvIv
S. K. Vaidya and N. A. Dani, “Cordial and 3-equitable graphs induced by duplication of edge”, Mathematics today, vol. 27, pp. 71-82, 2011.
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Copyright (c) 2020 Muhammad Naeem, Muhammad Kamran Siddiqui, Abdul Qudair Baig
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