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A lower bound and several exact results on the d-lucky number

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  • Klavžar, Sandi
  • Rajasingh, Indra
  • Emilet, D. Ahima

Abstract

If ℓ:V(G)→N is a vertex labeling of a graph G=(V(G),E(G)), then the d-lucky sum of a vertex u ∈ V(G) is dℓ(u)=dG(u)+∑v∈N(u)ℓ(v). The labeling ℓ is a d-lucky labeling if dℓ(u) ≠ dℓ(v) for every uv ∈ E(G). The d-lucky number ηdl(G) of G is the least positive integer k such that G has a d-lucky labeling V(G) → [k]. A general lower bound on the d-lucky number of a graph in terms of its clique number and related degree invariants is proved. The bound is sharp as demonstrated with an infinite family of corona graphs. The d-lucky number is also determined for the so-called Gm,n-web graphs and graphs obtained by attaching the same number of pendant vertices to the vertices of a generalized cocktail-party graph.

Suggested Citation

  • Klavžar, Sandi & Rajasingh, Indra & Emilet, D. Ahima, 2020. "A lower bound and several exact results on the d-lucky number," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307520
    DOI: 10.1016/j.amc.2019.124760
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    References listed on IDEAS

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    1. Lozano, Antoni & Mora, Mercè & Seara, Carlos, 2019. "Antimagic labelings of caterpillars," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 734-740.
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