Super (a, d)-G + e-antimagic total labeling of Gu[Sn]

• Rajkumar, S. ^[1] ; Nalliah, M. ^[1] ; Uma Maheswari, G. ^[2]
  1. [1] Vellore Institute of Technology.
  2. [2] Dhanalakshmi Srinivasan college of Engineering and Technology.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 1, 2022, págs. 249-262
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5014
• Enlaces
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• Resumen

  • Let G = (V, E) be a simple graph and H be a subgraph of G. Then G admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bijection ƒ : V (G) ∪ E(G) → {1, 2, 3, ..., |V (G)| + |E(G)|} such that for all subgraphs H’ of G isomorphic to H, the H’ weights w(H’) = .∑v∈V(H’) ƒ(v) +∑e∈E(H’) ƒ(e) constitute an arithmetic progression {a, a + d, a + 2d, ..., a + (n − 1)d}, where a and d are positive integers and n is the number of subgraphs of G isomorphic to H. The labeling ƒ is called a super (a, d)-H-antimagic total labeling if ƒ (V (G)) = {1, 2, 3, ..., |V (G)|}. In [9], authors have posed an open problem to characterize the super (a, d)-G+ e-antimagic total labeling of the graph Gu[Sn], where n ≥ 3 and 4 ≤ d ≤ p+q + 2. In this paper, a partial solution to this problem is obtained.

• Referencias bibliográficas
  • A. Ahmad, M. Bača, M. Lascsáková and A. Semaničová-Feňovčíková, “Super magic and antimagic labelings of disjoint union of plane graphs”, Science...
  • M. Bača, M. Numan and A. Semaničová-Feňovčíková, “Super d-antimagic labelings of disjoint union of generalized prisms”, Utilitas mathematica,...
  • G. Chartrand and L. Lesniak, Graphs & Digraphs, 4th ed. Boca Raton: CRC Press, 2005.
  • S. David Laurence and K. M. Kathiresan, “On super (A,d)-ph-antimagic total labeling of stars”, AKCE International journal of graphs and combinatorics,...
  • J. A. Gallian, “A dynamic survey of graph labelling”, The electronic journal of combinatorics, #DS6, 2020.
  • A. Gutiérrez and A. Lladó, “Magic coverings”, Journal of combinatorial mathematics and combinatorial computing, vol. 55, pp. 43-56, 2005.
  • N. Hartsfield and G. Ringel, Pearls in graph theory, Boston: Academic Press, 1994.
  • N. Inayah, A. N. M. Salman, R. Simanjuntak, “On (a, d)-H-antimagic coverings of graphs”, Journal of combinatorial mathematics and combinatorial...
  • K. Kathiresan and S. D. Laurence, “On super (a, d)-H-antimagic total covering of star related graphs”, Discussiones mathematicae graph theory,...
  • A. Kotzig and A. Rosa, “Magic valuations of finite graphs”, Canadian mathematical bulletin, vol. 13, no. 4, pp. 451–461, 1970. https://doi.org/10.4153/cmb-1970-084-1
  • K.-W Lih, “On magic and consecutive labelings of plane graphs”, Utilitas mathematica, vol. 24, pp. 165-197, 1983.
  • S. K. Patel and J. Vasava, “Some results on (a, d)-distance antimagic labeling”, Proyecciones (Antofagasta), vol. 39, no. 2, pp. 361–381,...
  • R. Simanjuntak, M. Miller and F. Bertault, “Two new (a, d)-antimagic graph labelings”, in Proceedings of the Eleventh Australasian Workshop...
  • K. A. Sugeng, M. Miller, Slamin, and M. Bača, “(a,d)-edge-antimagic total labelings of Caterpillars”, Lecture Notes in Computer Science, vol....