Abstract
A graph G of order p and size q is called (a, d)-edge-antimagic total if there exists a bijective function \(f: V (G) \cup E(G) \rightarrow \{ 1,2,\ldots,p + q\}\) such that the edge-weights \(wt_{f}(uv) = f(u) + f(uv) + f(v)\), uv ∈ E(G), form an arithmetic sequence with first term a and common difference d. The (a, d)-edge-antimagic total graph G is called super if the smallest possible labels appear on the vertices. In this paper, we study the existence of such labelings for Toeplitz graphs for several differences d.
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Notes
- 1.
The research for this article was supported by Slovak VEGA Grant 1/0130/12 and Higher Education Commission Pakistan Grant HEC(FD)/2007/555.
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Bača, M., Bashir, Y., Nadeem, M.F., Shabbir, A. (2015). On Super Edge-Antimagic Total Labeling of Toeplitz Graphs. In: Cartier, P., Choudary, A., Waldschmidt, M. (eds) Mathematics in the 21st Century. Springer Proceedings in Mathematics & Statistics, vol 98. Springer, Basel. https://doi.org/10.1007/978-3-0348-0859-0_1
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