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

Authors

  • S. Rajkumar Vellore Institute of Technology.
  • M. Nalliah Vellore Institute of Technology.
  • G. Uma Maheswari Dhanalakshmi Srinivasan college of Engineering and Technology.

DOI:

https://doi.org/10.22199/issn.0717-6279-5014

Keywords:

H-covering, super (a, d)-H-antimagic, star graphs

Abstract

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.

Author Biographies

S. Rajkumar, Vellore Institute of Technology.

Department of Mathematics, School of Advanced Sciences.

M. Nalliah, Vellore Institute of Technology.

Department of Mathematics, School of Advanced Sciences.

G. Uma Maheswari, Dhanalakshmi Srinivasan college of Engineering and Technology.

Department of Mathematics.

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Published

2022-01-28

How to Cite

[1]
S. Rajkumar, M. Nalliah, and G. Uma Maheswari, “Super (a, d)-G + e-antimagic total labeling of Gu[Sn]”, Proyecciones (Antofagasta, On line), vol. 41, no. 1, pp. 249-262, Jan. 2022.

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Artículos