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

Sandi Klavžar, Indra Rajasingh and D. Ahima Emilet

Applied Mathematics and Computation, 2020, vol. 366, issue C

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.

Keywords: Lucky labeling; d-lucky labeling; Corona graphs; Cocktail-party graphs (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307520

DOI: 10.1016/j.amc.2019.124760

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