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
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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.